arXiv daily: Quantum Physics

arXiv daily: Quantum Physics (quant-ph)

1.Quantum defogging: temporal photon number fluctuation correlation in time-variant fog scattering medium

Authors:Deyang Duan, Yuge Li, Yunjie Xia

Abstract: The conventional McCartney model simplifies fog as a scattering medium with space-time invariance, as the time-variant nature of fog is a pure noise for classical optical imaging. In this letter, an opposite finding to traditional idea is reported. The time parameter is incorporated into the McCartney model to account for photon number fluctuation introduced by time-variant fog. We demonstrated that the randomness of ambient photons in the time domain results in the absence of a stable correlation, while the scattering photons are the opposite. This difference can be measured by photon number fluctuation correlation when two conditions are met. A defogging image is reconstructed from the target's information carried by scattering light. Thus, the noise introduced by time-variant fog is eliminated by itself. Distinguishable images can be obtained even when the target is indistinguishable by conventional cameras, providing a prerequisite for subsequent high-level computer vision tasks.

2.Transition role of entangled data in quantum machine learning

Authors:Xinbiao Wang, Yuxuan Du, Zhuozhuo Tu, Yong Luo, Xiao Yuan, Dacheng Tao

Abstract: Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.

3.Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors

Authors:Daniel Bochen Tan, Dolev Bluvstein, Mikhail D. Lukin, Jason Cong

Abstract: Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfactory modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.

4.Suppression of high-frequency components in off-resonant modulated driving protocols for Rydberg blockade gate

Authors:Yuan Sun

Abstract: In the rapid development of cold atom qubit platform, the two-qubit Controlled-PHASE Rydberg blockade gate via off-resonant modulated driving has been making significant progress recently. In pursuit of higher fidelity, faster operation and better robustness, a major upgrade about suppression of high-frequency components in the modulation is called for, and a systematic method has been established here for this purpose. The quintessence of this newly constructed method can be interpreted as filtering out the relatively high frequency ingredients embedded in basis functions to generate the modulation waveforms and then analyzing whether they fulfill the requirement of gate condition. It turns out that appropriate waveforms of two-qubit entangling gate protocols can be successfully established via these frequency-adjusted basis functions, with the help of numerical optimization procedures. Moreover, this timely upgrade version can be further enhanced with adaptions to specific finite Rydberg blockade strength values and dual-pulse technique to overcome residual thermal motion of qubit atoms. Besides theoretical derivations, we also thoroughly investigate the representative modulation patterns, demonstrating the versatility of off-resonant modulated driving method in the design of two-qubit entangling Rydberg blockade gate.

5.Set Theory and Many Worlds

Authors:Paul Tappenden

Abstract: The 2022 Tel Aviv conference on the Many Worlds interpretation of quantum mechanics highlighted many differences between theorists. A very significant dichotomy is between Everettian fission (splitting) and Saunders-Wallace-Wilson divergence. For fission, an observer may have multiple futures, whereas for divergence they always have a single future. Divergence was explicitly introduced to resolve the problem of pre-measurement uncertainty for Everettian theory, which is universally believed to be absent for fission. Here, I maintain that there is indeed uncertainty about future observations prior to fission, so long as objective probability is a property of Everettian branches. This is made possible if the universe is a set and branches are subsets with probability measure. A universe which is a set of universes which are macroscopically isomorphic and span all possible configurations of microscopic local be\"ables fulfils that role. If objective probability is a property of branches, a successful Deutsch-Wallace decision-theoretic argument would justify the Principal Principle and be part of probability theory rather than being specific to Many Worlds. Any macroscopic object in our environment becomes a set of isomorphs with different microscopic configurations, each in an elemental universe (elemental in the set-theoretic sense). This is similar to Many Interacting Worlds theory but the observer inhabits the set of worlds, not an individual world. An observer has many elemental bodies.

6.Topological correlation: anyonic states cannot be determined by local operations and classical communication

Authors:Cheng-Qian Xu, D. L. Zhou

Abstract: Anyonic system not only has potential applications in the construction of topological quantum computer, but also presents a unique property known as topological entanglement entropy in quantum many-body systems. How to understand topological entanglement entropy is one of the most concerned problems for physicists. For an anyonic bipartite system, we define an operational measure of topological correlation based on the principle of maximal entropy, where the topological correlation is the information that cannot be accessed by local operations constrained by anyonic superselection rules and classical communication. This measure can be extended to measure non-local resources of other compound quantum systems in the presence of superselection rules. For a given anyonic bipartite state with maximal rank, we prove that its topological correlation is equal to its entropy of anyonic charge entanglement that has been shown in the literature to be able to derive topological entanglement entropy. This measure provides a more refined classification of correlations in a multipartite system with superselection rules and an illuminating approach to topological phase classification.

7.Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics

Authors:Frederik vom Ende

Abstract: We generalize the recent result that all analytic quantum dynamics can be represented exactly as the reduction of unitary dynamics generated by a time-dependent Hamiltonian. More precisely, we prove that the partial trace over analytic paths of unitaries can approximate any Lipschitz-continuous quantum dynamics arbitrarily well. We conclude by discussing potential improvements and generalizations of these results, their limitations, and the general challenges one has to overcome when trying to relate dynamics to quantities on the system-environment level.

8.Tensor network algorithm for simulating experimental Gaussian boson sampling

Authors:Changhun Oh, Minzhao Liu, Yuri Alexeev, Bill Fefferman, Liang Jiang

Abstract: Gaussian boson sampling is a promising candidate for showing experimental quantum advantage. While there is evidence that noiseless Gaussian boson sampling is hard to efficiently simulate using a classical computer, the current Gaussian boson sampling experiments inevitably suffer from loss and other noise models. Despite a high photon loss rate and the presence of noise, they are currently claimed to be hard to classically simulate with the best-known classical algorithm. In this work, we present a classical tensor-network algorithm that simulates Gaussian boson sampling and whose complexity can be significantly reduced when the photon loss rate is high. By generalizing the existing thermal-state approximation algorithm of lossy Gaussian boson sampling, the proposed algorithm enables us to achieve increased accuracy as the running time of the algorithm scales, as opposed to the algorithm that samples from the thermal state, which can give only a fixed accuracy. The generalization allows us to assess the computational power of current lossy experiments even though their output state is not believed to be close to a thermal state. We then simulate the largest Gaussian boson sampling implemented in experiments so far. Much like the actual experiments, classically verifying this large-scale simulation is challenging. To do this, we first observe that in our smaller-scale simulations the total variation distance, cross-entropy, and two-point correlation benchmarks all coincide. Based on this observation, we demonstrate for large-scale experiments that our sampler matches the ground-truth two-point and higher-order correlation functions better than the experiment does, exhibiting evidence that our sampler can simulate the ground-truth distribution better than the experiment can.

9.Universal Robust Geometric Quantum Control via Geometric Trajectory Correction

Authors:Tao Chen, Jia-Qi Hu, Chengxian Zhang, Zheng-Yuan Xue

Abstract: Universal robust quantum control is essential for performing complex quantum algorithms and efficient quantum error correction protocols. Geometric phase, as a key element with intrinsic fault-tolerant feature, can be well integrated into quantum control processes to enhance control robustness. However, the current geometric quantum control is still controversial in robust universality, which leads to the unsatisfactory result that cannot sufficiently enhance the robustness of arbitrary type of geometric gate. In this study, we find that the finite choice on geometric evolution trajectory is one of the main roots that constrain the control robustness of previous geometric schemes, as it is unable to optionally avoid some trajectory segments that are seriously affected by systematic errors. In view of this, we here propose a new scheme for universal robust geometric control based on geometric trajectory correction, where enough available evolution parameters are introduced to ensure that the effective correction against systematic errors can be executed. From the results of our numerical simulation, arbitrary type of geometric gate implemented by using the corrected geometric trajectory has absolute robustness advantages over conventional quantum one. In addition, we also verify the feasibility of the high-fidelity physical implementation of our scheme in superconducting quantum circuit, and finally discuss in detail the potential researches based on our scheme. Therefore, our theoretical work is expected to offer an attractive avenue for realizing practical fault-tolerant quantum computation in existing experimental platforms.

10.Architecture and protocols for all-photonic quantum repeaters

Authors:Naphan Benchasattabuse, Michal Hajdušek, Rodney Van Meter

Abstract: An all-photonic repeater scheme based on a type of graph state called a repeater graph state (RGS) promises tolerance to photon losses as well as operational errors, and offers a fast Bell pair generation rate, limited only by the RGS creation time (rather than enforced round-trip waits). Prior research on the topic has focused on the RGS generation and analyzing the secret key sharing rate, but there is a need to extend to use cases such as distributed computation or teleportation as will be used in a general-purpose Quantum Internet. Here, we propose a protocol and architecture that consider how end nodes participate in the connection; the capabilities and responsibilities of each node; the classical communications between nodes; and the Pauli frame correction information per end-to-end Bell pair. We give graphical reasoning on the correctness of the protocol via graph state manipulation rules. We then show that the RGS scheme is well suited to use in a link architecture connecting memory-based repeaters and end nodes for applications beyond secret sharing. Finally, we discuss the practicality of implementing our proposed protocol on quantum network simulators and how it can be integrated into an existing proposed quantum network architecture.

11.A Substrate Scheduler for Compiling Arbitrary Fault-tolerant Graph States

Authors:Sitong Liu, Naphan Benchasattabuse, Darcy QC Morgan, Michal Hajdušek, Simon J. Devitt, Rodney Van Meter

Abstract: Graph states are useful computational resources in quantum computing, particularly in measurement-based quantum computing models. However, compiling arbitrary graph states into executable form for fault-tolerant surface code execution and accurately estimating the compilation cost and the run-time resource cost remains an open problem. We introduce the Substrate Scheduler, a compiler module designed for fault-tolerant graph state compilation. The Substrate Scheduler aims to minimize the space-time volume cost of generating graph states. We show that Substrate Scheduler can efficiently compile graph states with thousands of vertices for "A Game of Surface Codes"-style patch-based surface code systems. Our results show that our module generates graph states with the lowest execution time complexity to date, achieving graph state generation time complexity that is at or below linear in the number of vertices and demonstrating specific types of graphs to have constant generation time complexity. Moreover, it provides a solid foundation for developing compilers that can handle a larger number of vertices, up to the millions or billions needed to accommodate a wide range of post-classical quantum computing applications.

12.Effects of Markovian noise and cavity disorders on the entanglement dynamics of double Jaynes-Cummings models

Authors:Harsh Rathee, Kishore Thapliyal, Anirban Pathak

Abstract: Dynamics of double Jaynes-Cummings models are studied in the presence of Markovian noise and cavity disorders with specific attention to entanglement sudden death and revivals. The study is focused on the glassy disorders, which remain unchanged during the observations. The field is initially assumed to be in a vacuum state, while the atoms are considered to be in a specific two-qubit superposition state. Specifically, the study has revealed that the presence of noise, or a nonlinear pump results in interesting behaviors in the entanglement dynamics. Further, entanglement sudden death is observed in the presence of Markovian noise and nonlinear pump. The presence of entanglement sudden deaths and revivals have also been observed in cases where they were absent initially for the chosen states. The effect of noise on the dynamics of the system is to decay the characteristics, while that of the disorder is to wash them out. On the other hand, the introduction of nonlinearity is found to cause the dynamics of the system to speed up.

13.Noise and dissipation on a moving mirror induced by the dynamical Casimir emission

Authors:Salvatore Butera

Abstract: We adopt an open quantum system approach to study the effects of the back-reaction from a quantum field onto the dynamics of a moving mirror. We describe the coupling between the mirror and the field by using a microscopic model from which the dielectric response of the mirror is obtained from first principles. Using second-order perturbation theory, we derive the master equation governing the mechanical motion of the mirror. Our analysis reveals that the mirror experiences coloured noise and non-local dissipation, which originate from the emission of particle pairs via the dynamical Casimir effect. We show that the noise and dissipation kernels, that enter in the definition of the time-dependent coefficients of the master equation, are related by fluctuation-dissipation relations.

14.Connecting classical finite exchangeability to quantum theory

Authors:Alessio Benavoli, Alessandro Facchini, Marco Zaffalon

Abstract: Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti's theorem provides a representation of infinitely exchangeable sequences of random variables as mixtures of independent and identically distributed variables. The quantum de Finetti theorem extends this result to symmetric quantum states on tensor product Hilbert spaces. However, both theorems do not hold for finitely exchangeable sequences. The aim of this work is to investigate two lesser-known representation theorems. Developed in classical probability theory, they extend de Finetti's theorem to finitely exchangeable sequences by using quasi-probabilities and quasi-expectations. With the aid of these theorems, we illustrate how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory (with boson-symmetric density matrices).

15.Quantum Computation and Simulation using Fermion-Pair Registers

Authors:Xiangkai Sun, Di Luo, Soonwon Choi

Abstract: We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where tightly localized fermion pairs are used to encode qubits exhibiting long coherence time and robustness against laser intensity noise. We describe how to engineer the SWAP gate and high-fidelity controlled-phase gates by adjusting the fermion hopping as well as Feshbach interaction strengths. Combined with previously demonstrated single-qubit rotations, these gates establish the computational universality of the system. Furthermore, we show that 2D quantum Ising Hamiltonians with tunable transverse and longitudinal fields can be efficient simulated by modulating Feshbach interaction strengths. We present a sample-efficient protocol to characterize engineered gates and Hamiltonian dynamics based on an improved classical shadow process tomography that requires minimal experimental controls. Our work opens up new opportunities to harness existing ultracold quantum gases for quantum information sciences.

1.Go-No go criteria for performing quantum chemistry calculations on quantum computers

Authors:Thibaud Louvet, Thomas Ayral, Xavier Waintal

Abstract: Quantum chemistry is envisioned as an early and disruptive application where quantum computers would provide a genuine advantage with respect to purely classical approaches. In this work, we propose two criteria for evaluating the potential of the two leading quantum approaches for this class of problems. The first criterion applies to the Variational Quantum Eigensolver (VQE) algorithm and sets an upper bound to the level of noise that can be tolerated in quantum hardware as a function of the target precision and problem size. We find a crippling effect of noise with an overall scaling of the precision that is generically less favourable than in the corresponding classical algorithms. This is due to the studied molecule being unrelated to the hardware dynamics, hence its noise; conversely the hardware noise populates states of arbitrary energy of the studied molecule. The second criterion applies to the Quantum Phase Estimation (QPE) algorithm that is often presented as the go-to replacement of VQE upon availability of (noiseless) fault-tolerant quantum computers. QPE suffers from the phenomenon known as the orthogonality catastrophe that generically leads to an exponentially small success probability when the size of the problem grows. Our criterion allows one to estimate quantitatively the importance of this phenomenon from the knowledge of the variance of the energy of the input state used in the calculation.

2.Decay and revival dynamics of a quantum state embedded in regularly spaced band of states

Authors:Jan Petter Hansen, Konrad Tywoniuk

Abstract: The dynamics of a single quantum state embedded in one or several (quasi-)continua is one of the most studied phenomena in quantum mechanics. In this work we investigate its discrete analogue and consider short and long time dynamics based on numerical and analytical solutions of the Schr\"odinger equation. In addition to derivation of explicit conditions for initial exponential decay, it is shown that a recent model of this class [Phys. Rev. A 95, 053821, (2017)], describing a qubit coupled to a phonon reservoir with energy dependent coupling parameters is identical to a qubit interacting with a finite number of parallel regularly spaced band of states via constant couplings. As a consequence, the characteristic near periodic initial state revivals can be viewed as a transition of probability between different continua via the reviving initial state. Furthermore, the observation of polynomial decay of the reviving peaks is present in any system with constant and sufficiently strong coupling.

3.Interferometric phase estimation and quantum resources dynamics in Bell coherent-states superpositions generated via a unitary beam splitter

Authors:Abdallah Slaoui, Brahim Amghar, Rachid Ahl Laamara

Abstract: Beam splitters are optical elements widely used in modern technological applications to split the initial light beam into a required number of beams and they play a very promising role for generating entangled optical states. Here, a potential scheme is proposed to generate Bell coherent-states superpositions through the action of a beam splitter when a Glauber coherent state is injected on one input mode and vacuum state is incident on the other one. Different quantifiers are used to measure the quantumness in the output state such as concurrence entanglement, entropic quantum discord, quantum coherence, geometric measure of quantum discord, local quantum uncertainty (LQU) and local quantum Fisher information. Thereby, we derive their analytical formulas and focus more on the behavior and bounds of each measure. Besides, we have introduced the notion of "weak measurement-induced LQU" captured by weak measurements as the generalization of normal LQU defined for standard projective measurement, and we investigate the effect of the measurement strength on the estimated phase enhancement if the generated Bell cat states are the probe states in quantum metrology. Our results suggest that the sensitivity of the interferometric phase estimation depends on how strongly one perturbs the probe state and that a weak measurement does not necessarily capture more quantumness in composite system.

4.Quantum operations with the time axis in a superposed direction

Authors:Seok Hyung Lie, M. S. Kim

Abstract: In the quantum theory, it has been shown that one can see if a process has the time reversal symmetry by applying the matrix transposition and examine if it remains physical. However, recent discoveries regarding the indefinite causal order of quantum processes suggest that there may be other, more general symmetry transformations of time besides the complete reversal. In this work, we introduce an expanded concept of matrix transposition, the generalized transposition, that takes into account general bipartite unitary transformations of a quantum operation's future and past Hilbert spaces, allowing for making the time axis definitely lie in a superposed direction, which generalizes the previously studied `indefinite direction of time', i.e., superposition of the forward and the backward time evolution. This framework may have applications in approaches that treat time and space equally like quantum gravity, where the spatio-temporal structure is explained to emerge from quantum mechanics. We apply this generalized transposition to investigate a continuous generalization of perfect tensors, a dynamic version of tracing out a subsystem, and the compatibility of multiple time axes in bipartite quantum interactions. Notably, we demonstrate that when a bipartite interaction is consistent with more distinct local temporal axes, there is a reduced allowance for information exchange between the two parties in order to prevent causality violations.

5.Near-Optimal Quantum Coreset Construction Algorithms for Clustering

Authors:Yecheng Xue, Xiaoyu Chen, Tongyang Li, Shaofeng H. -C. Jiang

Abstract: $k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for $k$-clustering in $\mathbb{R}^d$ with $\tilde{O}(\sqrt{nk}d^{3/2})$ query complexity. Our coreset reduces the input size from $n$ to $\mathrm{poly}(k\epsilon^{-1}d)$, so that existing $\alpha$-approximation algorithms for clustering can run on top of it and yield $(1 + \epsilon)\alpha$-approximation. This eventually yields a quadratic speedup for various $k$-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make $\Omega(\sqrt{nk})$ queries in order to achieve even $O(1)$-approximation for $k$-clustering.

6.Limitations of Noisy Quantum Devices in Computational and Entangling Power

Authors:Yuxuan Yan, Zhenyu Du, Junjie Chen, Xiongfeng Ma

Abstract: Quantum computing devices have been rapidly developed in the past decade. Tremendous efforts have been devoted to finding quantum advantages for useful but classically intractable problems via current noisy quantum devices without error correction. It is important to know the fundamental limitations of noisy quantum devices with the help of classical computers. For computation with general classical processing, we show that noisy quantum devices with a circuit depth of more than $O(\log n)$ provide no advantages in any quantum algorithms. This rigorously rules out the possibility of implementing well-known quantum algorithms, including Shor's, Grover's, Harrow-Hassidim-Lloyd, and linear-depth variational algorithms. Then, we study the maximal entanglement that noisy quantum devices can produce under one- and two-dimensional qubit connections. In particular, for a one-dimensional qubit chain, we show an upper bound of $O(\log n)$. This finding highlights the restraints for quantum simulation and scalability regarding entanglement growth. Additionally, our result sheds light on the classical simulatability in practical cases.

7.Multicone Diamond Waveguides for Nanoscale Quantum Sensing

Authors:Tianqi Zhu, Jan Rhensius, Viraj Damle, Konstantin Herb, Gabriel Puebla-Hellmann, Christian L. Degen, Erika Janitz

Abstract: The long-lived electronic spin of the nitrogen-vacancy (NV) center in diamond is a promising quantum sensor for detecting nanoscopic magnetic and electric fields in a variety of experimental conditions. Nevertheless, an outstanding challenge in improving measurement sensitivity is the poor signal-to-noise ratio (SNR) of prevalent optical spin-readout techniques. Here, we address this limitation by coupling individual NV centers to optimized diamond nanopillar structures, thereby improving optical collection efficiency of fluorescence. First, we optimize the structure in simulation, observing an increase in collection efficiency for tall ($\geq$ 5 $\mu$m) pillars with tapered sidewalls. We subsequently verify these predictions by fabricating and characterizing a representative set of structures using a reliable and reproducible nanofabrication process. An optimized device yields increased SNR, owing to improvements in collimation and directionality of emission. Promisingly, these devices are compatible with low-numerical-aperture, long-working-distance collection optics, as well as reduced tip radius, facilitating improved spatial resolution for scanning applications.

8.Accreditation of Analogue Quantum Simulators

Authors:Andrew Jackson, Theodoros Kapourniotis, Animesh Datta

Abstract: We present an accreditation protocol for analogue, i.e., continuous-time, quantum simulators. For a given simulation task, it provides an upper bound on the variation distance between the probability distributions at the output of an erroneous and error-free analogue quantum simulator. As its overheads are independent of the size and nature of the simulation, the protocol is ready for immediate usage and practical for the long term. It builds on the recent theoretical advances of strongly universal Hamiltonians and quantum accreditation as well as experimental progress towards the realisation of programmable hybrid analogue-digital quantum simulators.

9.Preserving a qubit during adjacent measurements at a few micrometers distance

Authors:Sainath Motlakunta, Nikhil Kotibhaskar, Chung-You Shih, Anthony Vogliano, Darian Mclaren, Lewis Hahn, Jingwen Zhu, Roland Hablützel, Rajibul Islam

Abstract: Protecting a quantum object against irreversible accidental measurements from its surroundings is necessary for controlled quantum operations. This becomes especially challenging or unfeasible if one must simultaneously measure or reset a nearby object's quantum state, such as in quantum error correction. In atomic systems - among the most established quantum information processing platforms - current attempts to preserve qubits against resonant laser-driven adjacent measurements waste valuable experimental resources such as coherence time or extra qubits and introduce additional errors. Here, we demonstrate high-fidelity preservation of an `asset' ion qubit while a neighboring `process' qubit is reset or measured at a few microns distance. We achieve $< 1\times 10^{-3}$ probability of accidental measurement of the asset qubit while the process qubit is reset, and $< 4\times 10^{-3}$ probability while applying a detection beam on the same neighbor for experimentally demonstrated fast detection times, at a distance of $6\ \rm{\mu m}$ or four times the addressing Gaussian beam waist. These low probabilities correspond to the preservation of the quantum state of the asset qubit with fidelities above $99.9\%$ (state reset) and $99.6\%$ (state measurement). Our results are enabled by precise wavefront control of the addressing optical beams while utilizing a single ion as a quantum sensor of optical aberrations. Our work demonstrates the feasibility of in-situ state reset and measurement operations, building towards enhancements in the speed and capabilities of quantum processors, such as in simulating measurement-driven quantum phases and realizing quantum error correction.

10.Quantization of counterexamples to Dirac's conjecture

Authors:Mauricio Valenzuela

Abstract: Dirac's conjecture, that secondary first-class constraints generate transformations that do not change the physical system's state, has various counterexamples. Since no matching gauge conditions can be imposed, the Dirac bracket cannot be defined, and restricting the phase space first and then quantizing is an inconsistent procedure. The latter observation has discouraged the study of systems of this kind more profoundly, while Dirac's conjecture is assumed generally valid. We point out, however, that secondary first-class constraints are just initial conditions that do not imply Poisson's bracket modification, and we carry out the quantization successfully by imposing these constraints on the initial state of the wave function. We apply the method to two Dirac's conjecture counterexamples, including Cawley's iconical system.

1.Numerical aspects of Casimir energy computation in acoustic scattering

Authors:Xiaoshu Sun, Timo Betcke, Alexander Strohmaier

Abstract: Computing the Casimir force and energy between objects is a classical problem of quantum theory going back to the 1940s. Several different approaches have been developed in the literature often based on different physical principles. Most notably a representation of the Casimir energy in terms of determinants of boundary layer operators makes it accessible to a numerical approach. In this paper, we first give an overview of the various methods and discuss the connection to the Krein-spectral shift function and computational aspects. We propose variants of Krylov subspace methods for the computation of the Casimir energy for large-scale problems and demonstrate Casimir computations for several complex configurations. This allows for Casimir energy calculation for large-scale practical problems and significantly speeds up the computations in that case.

2.A low-crosstalk double-side addressing system using acousto-optic deflectors for atomic ion qubits

Authors:Rui-Rui Li, Yi-Long Chen, Ran He, Shu-Qian Chen, Wen-Hao Qi, Jin-Ming Cui, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo

Abstract: The ability to individually and agilely manipulate qubits is crucial for the scalable trapped-ion quantum information processing. A plethora of challenging proposals have been demonstrated with the utilization of optical addressing systems, in which single ions is addressed exclusively by individual laser beam. However, crosstalk error in optical addressing systems limits the gate fidelity, becoming an obstacle to quantum computing, especially quantum error correction. In this work, we demonstrate a low-crosstalk double-side addressing system based on a pair of acousto-optic deflectors (AODs). The AODs addressing method can flexibly and parallelly address arbitrary ions between which the distance is variable in a chain. We employ two 0.4~NA objective lenses in both arms of the Raman laser and obtain a beam waist of 0.95~$\mu\mathrm{m}$, resulting in a Rabi rate crosstalk as low as $6.32\times10^{-4}$ when the neighboring ion separation is about 5.5~$\mu\mathrm{m}$. This agile and low-crosstalk double-side addressing system is promising for higher-fidelity gates and the practical application of the quantum error correction.

3.Revisiting weak values through non-normality

Authors:Lorena Ballesteros Ferraz, Riccardo Muolo, Yves Caudano, Timoteo Carletti

Abstract: Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify measured signals by exploiting a quantity called a weak value, but also to overcome philosophical difficulties related to the system perturbation induced by the measurement process. The method finds many applications and raises many philosophical questions as well, especially about the proper interpretation of the observations. In this paper, we show that any weak value can be expressed as the expectation value of a suitable non-normal operator. We propose a preliminary explanation of their anomalous and amplification behavior based on the theory of non-normal matrices and their link with non-normality: the weak value is different from an eigenvalue when the operator involved in the expectation value is non-normal. Our study paves the way for a deeper understanding of the measurement phenomenon, helps the design of experiments, and it is a call for collaboration to researchers in both fields to unravel new quantum phenomena induced by non-normality.

4.Entanglement and Teleportation in a 1-D Network with Repeaters

Authors:Ganesh Mylavarapu, Indranil Chakrabarty, Kaushiki Mukherjee, Minyi Huang, Junde Wu

Abstract: The most simplest form of quantum network is an one dimensional quantum network with a single player in each node. In remote entanglement distribution each of the players carry out measurement at the intermediate nodes to produce an entangled state between initial and final node which are remotely separated. It is imperative to say that the flow of information as well as the percolation of entanglement in a network between the source and target node is an important area of study. This will help us to understand the limits of the resource states as well as the measurements that are carried out in the process of remote entanglement distribution. In this article we investigate how the concurrence of the final entangled state obtained is connected with the concurrences of the initial entangled states present in a 1-D chain. We extend the works done for the pure entangled states for mixed entangled states like Werner states, Bell diagonal states and for general mixed states. We did not limit ourselves to a situation where the measurements are happening perfectly. We also investigate how these relations change when we consider imperfect swapping. We obtain the limits on the number of swappings as well as the success probability measurements to ensure the final state to be entangled state after swapping. In addition to these we also investigate on how much quantum information can be sent from the initial node to the final node (by computing the teleportation fidelity) when the measurement is perfect and imperfect with the same set of examples. Here also we obtain the limits on the number of swapping and the success probability of measurement to ensure that the final state obtained is capable of transferring the information . These results have tremendous future applications in sending quantum information between two quantum processors in remote entangled distribution.

5.Topological methods for studying contextuality: $N$-cycle scenarios and beyond

Authors:Aziz Kharoof, Selman Ipek, Cihan Okay

Abstract: Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize non-signaling distributions on contextuality scenarios. This paper studies simplicial distributions on $2$-dimensional measurement spaces by introducing new topological methods. Two key ingredients are a geometric interpretation of Fourier--Motzkin elimination and a technique based on collapsing of measurement spaces. Using the first one, we provide a new proof of Fine's theorem characterizing non-contextual distributions on $N$-cycle scenarios. Our approach goes beyond these scenarios and can describe non-contextual distributions on scenarios obtained by gluing cycle scenarios of various sizes. The second technique is used for detecting contextual vertices and deriving new Bell inequalities. Combined with these methods, we explore a monoid structure on simplicial distributions.

6.Interaction induced phase transition in quantum many-body detection probability

Authors:Archak Purkayastha, Alberto Imparato

Abstract: We introduce and explore the physics of quantum many-body detection probability (QMBDP). Imagine a quantum many-body system starting from a far-from-equilibrium initial state. Few detectors are put at some given positions of the system. The detectors make simultaneous stroboscopic projective measurements of some chosen local operators. A particular measurement outcome is taken as the `signal'. By QMBDP we refer to the probability that the signal is detected within a given time. We find that, due to repeated stroboscopic measurements, there can emerge a time-scale within which the signal is almost certainly detected. Depending on the spectral properties of the Hamiltonian, there can be a phase transition where this time-scale increases dramatically on tuning some Hamiltonian parameters across the transition point. Consequently, over a finite but large regime of time, depending on the initial state, tuning some Hamiltonian parameters can result in sharp transition from a phase where the signal is certainly detected (QMBDP $=1$) to a phase where the the signal may not be detected (QMBDP $<1$). As an example, we present a single-impurity non-integrable model where such a far-from-equilibrium transition is achieved by varying the many-body interaction strength.

7.Quantum spectral analysis by continuous measurement of Landau-Zener transitions

Authors:Christopher C. Bounds School of Physics and Astronomy, Monash University, Melbourne, Australia, Josh P. Duff School of Physics and Astronomy, Monash University, Melbourne, Australia, Alex Tritt School of Physics and Astronomy, Monash University, Melbourne, Australia, Hamish Taylor School of Physics and Astronomy, Monash University, Melbourne, Australia, George X. Coe School of Physics and Astronomy, Monash University, Melbourne, Australia, Sam J. White School of Physics and Astronomy, Monash University, Melbourne, Australia, Lincoln D. Turner School of Physics and Astronomy, Monash University, Melbourne, Australia

Abstract: We demonstrate the simultaneous estimation of signal frequency and amplitude by a single ensemble qubit sensor under irreducibly time-dependent control. Sweeping the qubit splitting linearly across a span induces a non-adiabatic Landau-Zener transition as the qubit crosses resonance. The signal frequency determines the time of the transition, and the amplitude its extent. Continuous weak measurement of this unitary evolution informs a parameter estimator retrieving precision measurements of frequency and amplitude. Implemented on radiofrequency-dressed ultracold atoms read out by a Faraday spin-light interface, we sense a magnetic signal with $\unit[20]{pT}$ precision in amplitude, and near-transform-limited precision in frequency, in a single $\unit[300]{ms}$ sweep from $\unit[7-13]{kHz}$. The protocol realises a swept-sine quantum spectrum analyzer, potentially sensing hundreds or thousands of channels with a single ensemble qubit.

8.Reduction of finite sampling noise in quantum neural networks

Authors:David Kreplin, Marco Roth

Abstract: Quantum neural networks (QNNs) use parameterized quantum circuits with data-dependent inputs and generate outputs through the evaluation of expectation values. Calculating these expectation values necessitates repeated circuit evaluations, thus introducing fundamental finite-sampling noise even on error-free quantum computers. We reduce this noise by introducing the variance regularization, a technique for reducing the variance of the expectation value during the quantum model training. This technique requires no additional circuit evaluations if the QNN is properly constructed. Our empirical findings demonstrate the reduced variance speeds up the training and lowers the output noise as well as decreases the number of measurements in the gradient circuit evaluation. This regularization method is benchmarked on the regression of multiple functions. We show that in our examples, it lowers the variance by an order of magnitude on average and leads to a significantly reduced noise level of the QNN. We finally demonstrate QNN training on a real quantum device and evaluate the impact of error mitigation. Here, the optimization is practical only due to the reduced number shots in the gradient evaluation resulting from the reduced variance.

9.Nonadiabatic nuclear-electron dynamics: a quantum computing approach

Authors:Arseny Kovyrshin, Mårten Skogh, Lars Tornberg, Anders Broo, Stefano Mensa, Emre Sahin, Benjamin C. B. Symons, Jason Crain, Ivano Tavernelli

Abstract: The combined quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling costs and therefore quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for the simulation of the time-evolution of molecular systems in the second quantization framework, which is applied to the simulation of the proton transfer dynamics in malonaldehyde. After partitioning the dynamics into slow and fast components, we show how the entanglement between the electronic and nuclear degrees of freedom can persist over long times if electrons are not adiabatically following the nuclear displacement. The proposed quantum algorithm may become a valid candidate for the study of electron-nuclear quantum phenomena when sufficiently powerful quantum computers become available.

10.Multichromatic Floquet engineering of quantum dissipation

Authors:François Impens, David Guéry-Odelin

Abstract: The monochromatic driving of a quantum system is a successful technique in quantum simulations, well captured by an effective Hamiltonian approach, and with applications in artificial gauge fields and topological engineering. In this letter, we investigate the modeling of multichromatic Floquet driving for the slow degrees of freedom. Within a well-defined range of parameters, we show that the time coarse-grained dynamics of such a driven closed quantum system is encapsulated in an effective Master equation for the time-averaged density matrix, that evolves under the action of an effective Hamiltonian and tunable Lindblad-type dissipation/quantum gain terms. As an application, we emulate the dissipation induced by phase noise and incoherent emission/absorption processes in the bichromatic driving of a two-level system.

11.Efficient Quantum State Synthesis with One Query

Authors:Gregory Rosenthal

Abstract: We present a polynomial-time quantum algorithm making a single query (in superposition) to a classical oracle, such that for every state $|\psi\rangle$ there exists a choice of oracle that makes the algorithm construct an exponentially close approximation of $|\psi\rangle$. Previous algorithms for this problem either used a linear number of queries and polynomial time [arXiv:1607.05256], or a constant number of queries and polynomially many ancillae but no nontrivial bound on the runtime [arXiv:2111.02999]. As corollaries we do the following: - We simplify the proof that statePSPACE $\subseteq$ stateQIP [arXiv:2108.07192] (a quantum state analogue of PSPACE $\subseteq$ IP) and show that a constant number of rounds of interaction suffices. - We show that QAC$\mathsf{_f^0}$ lower bounds for constructing explicit states would imply breakthrough circuit lower bounds for computing explicit boolean functions. - We prove that every $n$-qubit state can be constructed to within 0.01 error by an $O(2^n/n)$-size circuit over an appropriate finite gate set. More generally we give a size-error tradeoff which, by a counting argument, is optimal for any finite gate set.

12.Fast quantum state preparation and bath dynamics using non-Gaussian variational ansatz and quantum optimal control

Authors:Liam J. Bond, Arghavan Safavi-Naini, Jiří Minář

Abstract: We combine quantum optimal control with a variational ansatz based on non-Gaussian states for fast, non-adiabatic preparation of quantum many-body states. We demonstrate this on the example of the spin-boson model, and use a multi-polaron ansatz to prepare near-critical ground states. For one mode, we achieve a reduction in infidelity of up to $\approx 60$ ($\approx 20$) times compared to linear (optimised local adiabatic) ramps respectively; for many modes we achieve a reduction in infidelity of up to $\approx 5$ times compared to non-adiabatic linear ramps. Further, we show that the typical control quantity, the leakage from the variational manifold, provides only a loose bound on the state's fidelity. Instead, in analogy to the bond dimension of matrix product states, we suggest a controlled convergence criterion based on the number of polarons. Finally, motivated by the possibility of realizations in trapped ions, we study the dynamics of a system with bath properties going beyond the paradigm of (sub/super) Ohmic couplings. We apply the ansatz to the study of the out-of-time-order-correlator (OTOC) of the bath modes in a non-perturbative regime. The scrambling time is found to be a robust feature only weakly dependent on the details of the coupling between the bath and the spin.

1.Relational superposition measurements with a material quantum ruler

Authors:Hui Wang, Flaminia Giacomini, Franco Nori, Miles P. Blencowe

Abstract: In physics, it is crucial to identify operational measurement procedures to give physical meaning to abstract quantities. There has been significant effort to define time operationally using quantum systems, but the same has not been achieved for space. Developing an operational procedure to obtain information about the location of a quantum system is particularly important for a theory combining general relativity and quantum theory, which cannot rest on the classical notion of spacetime. Here, we take a first step towards this goal, and introduce a model to describe an extended material quantum system working as a position measurement device. Such a "quantum ruler" is composed of N harmonically interacting dipoles and serves as a (quantum) reference system for the position of another quantum system. We show that we can define a quantum measurement procedure corresponding to the "superposition of positions", and that by performing this measurement we can distinguish when the quantum system is in a coherent or incoherent superposition in the position basis. The model is fully relational, because the only meaningful variables are the relative positions between the ruler and the system, and the measurement is expressed in terms of an interaction between the measurement device and the measured system.

2.Self-duality and Jordan structure of quantum theory follow from homogeneity and pure transitivity

Authors:Howard Barnum, Cozmin Ududec, John van de Wetering

Abstract: Among the many important geometric properties of quantum state space are: transitivity of the group of symmetries of the cone of unnormalized states on its interior (homogeneity), identification of this cone with its dual cone of effects via an inner product (self-duality), and transitivity of the group of symmetries of the normalized state space on the pure normalized states (pure transitivity). Koecher and Vinberg showed that homogeneity and self-duality characterize Jordan-algebraic state spaces: real, complex and quaternionic quantum theory, spin factors, 3-dimensional octonionic quantum state space and direct sums of these irreducible spaces. We show that self-duality follows from homogeneity and pure transitivity. These properties have a more direct physical and information-processing significance than self-duality. We show for instance (extending results of Barnum, Gaebeler, and Wilce) that homogeneity is closely related to the ability to steer quantum states. Our alternative to the Koecher-Vinberg theorem characterizes nearly the same set of state spaces: direct sums of isomorphic Jordan-algebraic ones, which may be viewed as composites of a classical system with an irreducible Jordan-algebraic one. There are various physically and informationally natural additional postulates that are known to single out complex quantum theory from among these Jordan-algebraic possibilities. We give various such reconstructions based on the additional property of local tomography.

3.Efficient VQE Approach for Accurate Simulations on the Kagome Lattice

Authors:Jyothikamalesh S, Kaarnika A, Dr. Mohankumar. M, Sanjay Vishwakarma, Srinjoy Ganguly, Yuvaraj P

Abstract: The Kagome lattice, a captivating lattice structure composed of interconnected triangles with frustrated magnetic properties, has garnered considerable interest in condensed matter physics, quantum magnetism, and quantum computing.The Ansatz optimization provided in this study along with extensive research on optimisation technique results us with high accuracy. This study focuses on using multiple ansatz models to create an effective Variational Quantum Eigensolver (VQE) on the Kagome lattice. By comparing various optimisation methods and optimising the VQE ansatz models, the main goal is to estimate ground state attributes with high accuracy. This study advances quantum computing and advances our knowledge of quantum materials with complex lattice structures by taking advantage of the distinctive geometric configuration and features of the Kagome lattice. Aiming to improve the effectiveness and accuracy of VQE implementations, the study examines how Ansatz Modelling, quantum effects, and optimization techniques interact in VQE algorithm. The findings and understandings from this study provide useful direction for upcoming improvements in quantum algorithms,quantum machine learning and the investigation of quantum materials on the Kagome Lattice.

4.Graph decomposition techniques for solving combinatorial optimization problems with variational quantum algorithms

Authors:Moises Ponce, Rebekah Herrman, Phillip C. Lotshaw, Sarah Powers, George Siopsis, Travis Humble, James Ostrowski

Abstract: The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum--in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly $k$-regular graphs, as $k$-regular graphs on $n$ vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. While this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.

5.Bidirectional quantum teleportation of even and odd coherent states through the multipartite Glauber coherent state: Theory and implementation

Authors:Nada Ikken, Abdallah Slaoui, Rachid Ahl Laamara, Lalla Btissam Drissi

Abstract: Quantum teleportation has become a fundamental building block of quantum technologies, playing a vital role in the development of quantum communication networks. Here, we present a bidirectional quantum teleportation (BQT) protocol that enables even and odd coherent states to be transmitted and reconstructed over arbitrary distances in two directions. To this end, we employ the multipartite Glauber coherent state, comprising the Greenberger-Horne-Zeilinger, ground and Werner states, as a quantum resource linking distant partners Alice and Bob. The pairwise entanglement existing in symmetric and antisymmetric multipartite coherent states is explored, and by controlling the overlap and number of probes constructing various types of quantum channels, the teleportation efficiency of teleported states in both directions may be maximized. Besides, Alice's and Bob's trigger phases are estimated to explore their roles in our protocol using two kinds of quantum statistical speed referred to as quantum Fisher information (QFI) and Hilbert-Schmidt speed (HSS). Specifically, we show that the lower bound of the statistical estimation error, quantified by QFI and HSS, corresponds to the highest fidelity from Alice to Bob and conversely from Bob to Alice, and that the choice of the pre-shared quantum channel has a critical role in achieving high BQT efficiency. Finally, we show how to implement the suggested scheme on current experimental tools, where Alice can transfer her even coherent state to Bob, and at the same time, Bob can transfer his odd coherent state to Alice.

6.Orthonormal bases of extreme spin coherence

Authors:Marcin Rudziński, Adam Burchardt, Karol Życzkowski

Abstract: Spin anticoherent states acquired recently a lot of attention as the most "quantum" states. Some coherent and anticoherent spin states are known as optimal quantum rotosensors. In this work we introduce a measure of spin coherence for orthonormal bases, determined by the average anticoherence of individual vectors, and identify the most and the least coherent bases which lead to orthogonal measurements of extreme coherence. Their symmetries can be revealed using the Majorana stellar representation, which provides an intuitive geometrical representation of a pure state by points on a sphere. Results obtained lead to maximally (minimally) entangled bases in the $2j+1$ dimensional symmetric subspace of the $2^{2j}$ dimensional space of quantum states of multipartite systems composed of $2j$ qubits.

7.Grüneisen parameter as an entanglement compass

Authors:Lucas Squillante, Luciano S. Ricco, Aniekan Magnus Ukpong, Roberto E. Lagos-Monaco, Antonio C. Seridonio, Mariano de Souza

Abstract: The Gr\"uneisen ratio $\Gamma$, i.e., the singular part of the ratio of thermal expansion to the specific heat, has been broadly employed to explore both finite-$T$ and quantum critical points (QCPs). For a genuine quantum phase transition (QPT), thermal fluctuations are absent and thus the thermodynamic $\Gamma$ cannot be employed. We propose a quantum analogue to $\Gamma$ that computes entanglement as a function of a tuning parameter and show that QPTs take place only for quadratic non-diagonal Hamiltonians. We showcase our approach using the quantum 1D Ising model with transverse field and Kane's quantum computer. The slowing down of the dynamics and thus the ``creation of mass'' close to any QCP/QPT is also discussed.

8.Metasurface-based hybrid optical cavities for chiral sensing

Authors:Nico S. Bassler, Andrea Aiello, Kai P. Schmidt, Claudiu Genes, Michael Reitz

Abstract: Quantum metasurfaces, i.e., two-dimensional subwavelength arrays of quantum emitters, can be employed as mirrors towards the design of hybrid cavities, where the optical response is given by the interplay of a cavity-confined field and the surface modes supported by the arrays. We show that, under external magnetic field control, stacked layers of quantum metasurfaces can serve as helicity-preserving cavities. These structures exhibit ultranarrow resonances and can enhance the intensity of the incoming field by orders of magnitude, while simultaneously preserving the handedness of the field circulating inside the resonator, as opposed to conventional cavities. The rapid phase shift in the cavity transmission around the resonance can be exploited for the sensitive detection of chiral scatterers passing through the cavity. We discuss possible applications of these resonators as sensors for the discrimination of chiral molecules.

9.$k$-positivity and Schmidt number under orthogonal group symmetries

Authors:Sang-Jun Park, Sang-Gyun Youn

Abstract: In this paper, we study $k$-positivity and Schmidt number under standard orthogonal group symmetries. The Schmidt number is a widely used measure of quantum entanglement in quantum information theory. First of all, we exhibit a complete characterization of all $k$-positive orthogonally covariant maps. This generalizes the earlier results in [Tom85]. Then, we optimize some averaging techniques to establish duality relations between orthogonally covariant maps and orthogonally invariant operators. This new framework enables us to effectively compute the Schmidt numbers of all orthogonally invariant quantum states.

10.Self-testing in prepare-and-measure scenarios and a robust version of Wigner's theorem

Authors:Miguel Navascues, Károly F. Pál, Tamás Vértesi, Mateus Araújo

Abstract: We consider communication scenarios where one party sends quantum states of known dimensionality $D$, prepared with an untrusted apparatus, to another, distant party, who probes them with uncharacterized measurement devices. We prove that, for any ensemble of reference pure quantum states, there exists one such prepare-and-measure scenario and a linear functional $W$ on its observed measurement probabilities, such that $W$ can only be maximized if the preparations coincide with the reference states, modulo a unitary or an anti-unitary transformation. In other words, prepare-and-measure scenarios allow one to "self-test" arbitrary ensembles of pure quantum states. Arbitrary extreme $D$-dimensional quantum measurements, or sets thereof, can be similarly self-tested. Our results rely on a robust generalization of Wigner's theorem, a known result in particle physics that characterizes physical symmetries.

11.Manipulating spatial structure of high-order quantum coherence with entangled photons

Authors:Shuang-Yin Huang, Jing Gao, Zhi-Cheng Ren, Zi-Mo Cheng, Wen-Zheng Zhu, Shu-Tian Xue, Yan-Chao Lou, Zhi-Feng Liu, Chao Chen, Fei Zhu, Li-Ping Yang, Xi-Lin Wang, Hui-Tian Wang

Abstract: High-order quantum coherence reveals the statistical correlation of quantum particles. Manipulation of quantum coherence of light in temporal domain enables to produce single-photon source, which has become one of the most important quantum resources. High-order quantum coherence in spatial domain plays a crucial role in a variety of applications, such as quantum imaging, holography and microscopy. However, the active control of high-order spatial quantum coherence remains a challenging task. Here we predict theoretically and demonstrate experimentally the first active manipulation of high-order spatial quantum coherence by mapping the entanglement of spatially structured photons. Our results not only enable to inject new strength into current applications, but also provide new possibilities towards more wide applications of high-order quantum coherence.

12.Non-perturbative theory of spontaneous parametric down-conversion in open and dispersive optical systems

Authors:Aleksa Krstić, Frank Setzpfandt, Sina Saravi

Abstract: We develop a non-perturbative formulation based on the Green-function quantization method, that can describe spontaneous parametric down-conversion in the high-gain regime in nonlinear optical structures with arbitrary amount of loss and dispersion. This formalism opens the way for description and design of arbitrary complex and/or open nanostructured nonlinear optical systems in quantum technology applications, such as squeezed-light generation, nonlinearity-based quantum sensing, and hybrid quantum systems mediated by nonlinear interactions. As an example case, we numerically investigate the scenario of integrated quantum spectroscopy with undetected photons, in the high-gain regime, and uncover novel gain-dependent effects in the performance of the system.

13.Fermonic anyons: entanglement and quantum computation from a resource-theoretic perspective

Authors:Allan Tosta, Antônio C. Lourenço, Daniel Brod, Fernando Iemini, Tiago Debarba

Abstract: Often quantum computational models can be understood via the lens of resource theories, where a computational advantage is achieved by consuming specific forms of quantum resources and, conversely, resource-free computations are classically simulable. For example, circuits of nearest-neighbor matchgates can be mapped to free-fermion dynamics, which can be simulated classically. Supplementing these circuits with nonmatchgate operations or non-gaussian fermionic states, respectively, makes them quantum universal. Can we similarly identify quantum computational resources in the setting of more general quasi-particle statistics, such as that of fermionic anyons? In this work, we develop a resource-theoretic framework to define and investigate the separability of fermionic anyons. We build the notion of separability through a fractional Jordan-Wigner transformation, leading to a Schmidt decomposition for fermionic-anyon states. We show that this notion of fermionic-anyon separability, and the unitary operations that preserve it, can be mapped to the free resources of matchgate circuits. We also identify how entanglement between two qubits encoded in a dual-rail manner, as standard for matchgate circuits, corresponds to the notion of entanglement between fermionic anyons. Though this does not coincide with the usual definition of qubit entanglement, it provides new insight into the limited capabilities of matchgate circuits.

14.Catalysis in Quantum Information Theory

Authors:Patryk Lipka-Bartosik, Henrik Wilming, Nelly H. Y. Ng

Abstract: Catalysts open up new reaction pathways which can speed up chemical reactions while not consuming the catalyst. A similar phenomenon has been discovered in quantum information science, where physical transformations become possible by utilizing a (quantum) degree of freedom that remains unchanged throughout the process. In this review, we present a comprehensive overview of the concept of catalysis in quantum information science and discuss its applications in various physical contexts.

15.Post-selection-free Measurement-Induced Phase Transition in Driven Atomic Gases with Collective Decay

Authors:Gianluca Passarelli, Xhek Turkeshi, Angelo Russomanno, Procolo Lucignano, Marco Schirò, Rosario Fazio

Abstract: We study the properties of a monitored ensemble of atoms driven by a laser field and in the presence of collective decay. By varying the strength of the external drive, the atomic cloud undergoes a measurement-induced phase transition separating two phases with entanglement entropy scaling sub-extensively with the system size. The critical point coincides with the transition to a superradiant spontaneous emission. Our setup is implementable in current light-matter interaction devices, and most notably, the monitored dynamics is free from the post-selection measurement problem, even in the case of imperfect monitoring.

16.Stochastic Mean-field Theory for Conditional Spin Squeezing by Homodyne Probing of Atom-Cavity Photon Dressed States

Authors:ZhiQing Zhang, Yuan Zhang, HaiZhong Guo, Lingrui Wang, Gang Chen, Chongxin Shan, Klaus Mølmer

Abstract: A projective measurement on a quantum system prepares an eigenstate of the observable measured. Measurements of collective observables can thus be employed to herald the preparation of entangled states of quantum systems with no mutual interactions. For large quantum systems numerical handling of the conditional quantum state by the density matrix becomes prohibitively complicated, but they may be treated by effective approximate methods. In this article, we present a stochastic variant of cumulant mean-field theory to simulate the effect of continuous optical probing of an atomic ensemble, which can be readily generalized to describe more complex systems, such as ensembles of multi-level systems and hybrid atomic and mechanical systems, and protocols that include adaptive measurements and feedback. We apply the theory to a system with tens of thousands of rubidium-87 atom in an optical cavity, and we study the spin squeezing occurring solely due to homodyne detection of a transmitted light signal near an atom-photon dressed state resonance, cf., a similar application of heterodyne detection to this system [Nat. Photonics, 8(9), 731-736 (2014)].

17.A general-purpose single-photon-based quantum computing platform

Authors:Nicolas Maring, Andreas Fyrillas, Mathias Pont, Edouard Ivanov, Petr Stepanov, Nico Margaria, William Hease, Anton Pishchagin, Thi Huong Au, Sébastien Boissier, Eric Bertasi, Aurélien Baert, Mario Valdivia, Marie Billard, Ozan Acar, Alexandre Brieussel, Rawad Mezher, Stephen C. Wein, Alexia Salavrakos, Patrick Sinnott, Dario A. Fioretto, Pierre-Emmanuel Emeriau, Nadia Belabas, Shane Mansfield, Pascale Senellart, Jean Senellart, Niccolo Somaschi

Abstract: Quantum computing aims at exploiting quantum phenomena to efficiently perform computations that are unfeasible even for the most powerful classical supercomputers. Among the promising technological approaches, photonic quantum computing offers the advantages of low decoherence, information processing with modest cryogenic requirements, and native integration with classical and quantum networks. To date, quantum computing demonstrations with light have implemented specific tasks with specialized hardware, notably Gaussian Boson Sampling which permitted quantum computational advantage to be reached. Here we report a first user-ready general-purpose quantum computing prototype based on single photons. The device comprises a high-efficiency quantum-dot single-photon source feeding a universal linear optical network on a reconfigurable chip for which hardware errors are compensated by a machine-learned transpilation process. Our full software stack allows remote control of the device to perform computations via logic gates or direct photonic operations. For gate-based computation we benchmark one-, two- and three-qubit gates with state-of-the art fidelities of $99.6\pm0.1 \%$, $93.8\pm0.6 \%$ and $86\pm1.2 \%$ respectively. We also implement a variational quantum eigensolver, which we use to calculate the energy levels of the hydrogen molecule with high accuracy. For photon native computation, we implement a classifier algorithm using a $3$-photon-based quantum neural network and report a first $6$-photon Boson Sampling demonstration on a universal reconfigurable integrated circuit. Finally, we report on a first heralded 3-photon entanglement generation, a key milestone toward measurement-based quantum computing.

1.Digital quantum simulator for the time-dependent Dirac equation using discrete-time quantum walks

Authors:Shigetora Miyashita, Takahiko Satoh, Michihiko Sugawara, Naphan Benchasattabuse, Ken M. Nakanishi, Michal Hajdušek, Hyensoo Choi, Rodney Van Meter

Abstract: We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in non-relativistic regimes efficiently. However, only some studies have attempted to simulate relativistic dynamics due to its theoretical and computational difficulty. By leveraging the convergence of discrete-time quantum walks to the Dirac equation, we develop a quantum spectral method that approximates smooth solutions with exponential convergence. This mitigates errors in implementing potential functions and reduces the overall gate complexity that depends on errors. We demonstrate that our approach does not require additional operations compared to the asymptotic gate complexity of non-relativistic real-space algorithms. Our findings indicate that simulating relativistic dynamics is achievable with quantum computers and can provide insights into relativistic quantum physics and chemistry.

2.Search for Multiple Adjacent Marked Vertices on the Hypercube by a Quantum Walk with Partial Phase Inversion

Authors:Luciano S. de Souza, Jonathan H. A. de Carvalho, Henrique C. T. Santos, Tiago A. E. Ferreira

Abstract: There is a strong interest in quantum search algorithms, particularly in problems with multiple adjacent solutions. In the hypercube, part of the energy of the quantum system is retained in states adjacent to the target states, decreasing the chances of the target states being observed. This paper applies the Multiself-loop Lackadaisical Quantum Walk with Partial Phase Inversion to search for multiple adjacent marked vertices on the hypercube. Aspects like the type of marked vertices are considered in addition to using multiple self-loops and weight compositions. Two scenarios are analyzed. Firstly, the relative position of non-adjacent marked vertices together with adjacent marked vertices. Secondly, only adjacent marked vertices are analyzed. Here, we show experimentally that, with partial phase inversion, a quantum walk can amplify the probability amplitudes of the target states, reaching success probabilities of values close to $1$. We also show that the relative position of non-adjacent marked vertices does not significantly influence the search results. Our results demonstrate that the partial phase inversion of target states is a promising alternative to search adjacent solutions with quantum walks, which is a key capacity for real search applications.

3.LEO Clock Synchronization with Entangled Light

Authors:Ronakraj Gosalia, Robert Malaney, Ryan Aguinaldo, Jonathan Green

Abstract: Precision navigation and timing, very-long-baseline interferometry, next-generation communication, sensing, and tests of fundamental physics all require a highly synchronized network of clocks. With the advance of highly-accurate optical atomic clocks, the precision requirements for synchronization are reaching the limits of classical physics (i.e. the standard quantum limit, SQL). Efficiently overcoming the SQL to reach the fundamental Heisenberg limit can be achieved via the use of squeezed or entangled light. Although approaches to the Heisenberg limit are well understood in theory, a practical implementation, such as in space-based platforms, requires that the advantage outweighs the added costs and complexity. Here, we focus on the question: can entanglement yield a quantum advantage in clock synchronization over lossy satellite-to-satellite channels? We answer in the affirmative, showing that the redundancy afforded by the two-mode nature of entanglement allows recoverability even over asymmetrically lossy channels. We further show this recoverability is an improvement over single-mode squeezing sensing, thereby illustrating a new complexity-performance trade-off for space-based sensing applications.

4.Continuous-Variable Quantum Key Distribution at 10 GBaud using an Integrated Photonic-Electronic Receiver

Authors:Adnan A. E. Hajomer, Cedric Bruynsteen, Ivan Derkach, Nitin Jain, Axl Bomhals, Sarah Bastiaens, Ulrik L. Andersen, Xin Yin, Tobias Gehring

Abstract: Quantum key distribution (QKD) is a well-known application of quantum information theory that guarantees information-theoretically secure key exchange. As QKD becomes more and more commercially viable, challenges such as scalability, network integration, and high production costs need to be addressed. Photonic and electronic integrated circuits that can be produced in large volumes at low cost hold the key to large-scale deployment of next-generation QKD systems. Here, we present a continuous-variable (CV) QKD system using an integrated photonic-electronic receiver that combines a silicon photonic integrated circuit implementing a phase-diverse receiver with custom-designed GaAs pHEMT transimpedance amplifiers. The QKD system operates at a classical telecom symbol rate of 10 GBaud, generating high secret key rates exceeding 0.7 Gb/s over a distance of 5 km and 0.3 Gb/s over a distance of 10 km. The secret keys are secure against collective attacks with finite-size effects taken into account. Well-designed digital signal processing enabled the high-speed operation. Our experiment sets a new record for secure quantum communication and paves the way for the next generation of CV-QKD systems.

5.Pure classical correlation dominant quantum thermal diode via three triangular-coupled qubits

Authors:Yi-jia Yang, Yu-qiang Liu, Chang-shui Yu

Abstract: A quantum thermal diode is designed based on three pairwise coupled qubits, two connected to a common reservoir and the other to an independent reservoir. It is found that the internal couplings between qubits can enhance heat currents. If the two identical qubits uniformly couple with the common reservoir, the crossing dissipation will occur, leading to the initial-state-dependent steady state, which can be decomposed into the mixture of two particular steady states: the heat-conducting state generating maximum heat current and the heat-resisting state not transporting heat. However, the rectification factor does not depend on the initial state. In particular, we find that neither quantum entanglement nor quantum discord is present in the steady state, but the pure classical correlation shows a remarkably consistent behavior as the heat rectification factor, which reveals the vital role of classical correlation in the system.

6.Tutorial: projector approach to open quantum systems

Authors:C. Gonzalez-Ballestero

Abstract: Most quantum theorists are familiar with different ways of describing the effective quantum dynamics of a system coupled to external degrees of freedom, such as the Born-Markov master equation or the adiabatic elimination. Understanding the deep connection between these apparently unrelated methods can be a powerful tool, allowing us to derive effective dynamics in unconventional systems or regimes. This tutorial aims at providing quantum theorists across multiple fields (e.g. quantum and atom optics, optomechanics, or hybrid quantum systems) with a self-contained practical toolbox to derive effective quantum dynamics, applicable to systems ranging from N-level emitters to mechanical resonators. This tutorial is written for any theorist working on applied quantum physics, from quantum and atom optics to optomechanics or hybrid quantum systems. First, we summarize the projector approach to open quantum systems and the derivation of the fundamental Nakajima-Zwanzig equation. Then, we show how three common effective equations, namely the Born-Markov Master Equation, the adiabatic elimination used in atom physics, and a different adiabatic elimination used in sideband cooling, can be derived from different perturbative expansions of the Nakajima-Zwanzig equation. We also solve in detail two specific examples using this formalism, namely the adiabatic elimination in a Lambda system and the effective equations of a mechanical resonator cooled by an optical cavity.

7.Monte-Carlo simulation method for the frequency comb spectrum of an atom laser

Authors:A. Schelle

Abstract: A theoretical particle-number conserving quantum field theory based on the concept of imaginary time is presented and applied to the scenario of a coherent atomic laser field at ultra-cold temperatures. The proposed theoretical model describes the analytical derivation of the frequency comb spectrum for an atomic laser realized from modeling a coherent atomic beam of condensate and non-condensate quantum field components released from a trapped Bose-Einstein condensate at a given repetition phase and frequency. The condensate part of the atomic vapor is assumed to be subjected to thermal noise induced by the temperature of the surrounding thermal atomic cloud. This new quantum approach uses time periodicity and an orthogonal decomposition in a complex-valued quantum field representation to derive and model the quantum field's forward- and backward-propagating components as a standing wave field in the same unique time and temperature domain without singularities at finite temperatures. The complex-valued atom laser field, the resulting frequency comb, and the repetition frequency distribution with the varying shape of envelopes are numerically monitored within a quantitative Monte-Carlo sampling method, as a function of temperature and trap frequency of the external confinement.

8.Effects of noise on performance of Bernstein-Vazirani algorithm

Authors:Archi Gupta, Priya Ghosh, Kornikar Sen, Ujjwal Sen

Abstract: The Bernstein-Vazirani algorithm offers exceptional accuracy in finding a hidden bit string of a function. We explore how the algorithm performs in real-world situations where noise can potentially interfere with the performance. In order to assess the impact of imperfect equipments, we introduce various forms of glassy disorders into the effect of the Hadamard gates used in Bernstein-Vazirani circuit. We incorporated disorders of five different forms, viz. Haar-uniform with finite cutoff, spherical Gaussian, discrete circular, spherical Cauchy-Lorentz, and squeezed. We find that the effectiveness of the algorithm decreases with increasing disorder strength in all cases. Additionally, we demonstrate that as the number of bits in the secret string increases, the success probability of correctly guessing the string becomes increasingly insensitive to the type of disorder and instead depends only on the center and spread of the disorder. We compare our results with the performance of the analogous classical algorithm in presence of similar noise. The classical algorithm becomes extremely inefficient for long secret strings, even in the noiseless scenario. Moreover, we witness that the Bernstein-Vazirani algorithm performs better than its classical counterpart for almost all types of disorder under consideration, for all disorder strengths. An instance where that is not the case is for strong discrete disorder with a moderate-sized hidden bit string.

9.A physical noise model for quantum measurements

Authors:Faedi Loulidi, Ion Nechita, Clément Pellegrini

Abstract: In this paper we introduce a novel noise model for quantum measurements motivated by an indirect measurement scheme with faulty preparation. Averaging over random dynamics governing the interaction between the quantum system and a probe, a natural, physical noise model emerges. We compare it to existing noise models (uniform and depolarizing) in the framework of incompatibility robustness. We observe that our model allows for larger compatibility regions for specific classes of measurements.

10.Variational quantum eigensolvers for the non-Hermitian systems by variance minimization

Authors:Xu-Dan Xie, Zheng-Yuan Xue, Dan-Bo Zhang

Abstract: Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the non-Hermitian Hamiltonian, as zero variance can naturally determine the eigenvalues and the associated left and right eigenstates. Moreover, the energy is set as a parameter in the cost function and can be tuned to obtain the whole spectrum, where each eigenstate can be efficiently obtained using a two-step optimization scheme. Through numerical simulations, we demonstrate the algorithm for preparing the left and right eigenstates, verifying the biorthogonal relations, as well as evaluating the observables. We also investigate the impact of quantum noise on our algorithm and show that its performance can be largely improved using error mitigation techniques. Therefore, our work suggests an avenue for solving non-Hermitian quantum many-body systems with variational quantum algorithms on near-term noisy quantum computers.

11.Demonstration of the quantum principle of least action with single photons

Authors:Yong-Li Wen, Yunfei Wang, Li-Man Tian, Shanchao Zhang, Jianfeng Li, Jing-Song Du, Hui Yan, Shi-Liang Zhu

Abstract: The principle of least action is arguably the most fundamental principle in physics as it can be used to derive the equations of motion in various branches of physics. However, this principle has not been experimentally demonstrated at the quantum level because the propagators for Feymann's path integrals have never been observed. The propagator is a fundamental concept and contains various significant properties of a quantum system in path integral formulation, so its experimental observation is itself essential in quantum mechanics. Here we theoretically propose and experimentally observe single photons' propagators based on the method of directly measuring quantum wave-functions. Furthermore, we obtain the classical trajectories of the single photons in free space and in a harmonic trap based on the extremum of the observed propagators, thereby experimentally demonstrating the quantum principle of least action. Our work paves the way for experimentally exploring fundamental problems of quantum theory in the formulation of path integrals.

12.Optoacoustic cooling of traveling hypersound waves

Authors:Laura Blázquez Martínez, Philipp Wiedemann, Changlong Zhu, Andreas Geilen, Birgit Stiller

Abstract: We experimentally demonstrate optoacoustic cooling via stimulated Brillouin-Mandelstam scattering in a 50 cm-long tapered photonic crystal fiber. For a 7.38 GHz acoustic mode, a cooling rate of 219 K from room temperature has been achieved. As anti-Stokes and Stokes Brillouin processes naturally break the symmetry of phonon cooling and heating, resolved sideband schemes are not necessary. The experiments pave the way to explore the classical to quantum transition for macroscopic objects and could enable new quantum technologies in terms of storage and repeater schemes.

13.Control of quantum coherence and Hong-Ou-Mandel interference of structured photon pairs

Authors:Dianzhen Cui, Xi-Lin Wang, X. X. Yi, Li-Ping Yang

Abstract: Accurately controlling quantum coherence and Hong-Ou-Mandel (HOM) interference of two-photon states is crucial for their applications in quantum sensing and quantum imaging. In this study, we have developed a comprehensive theory of HOM interference of three-dimensional (3D) structured photon pairs. Our findings reveal that the HOM dip and peak are primarily determined by the combined exchange-reflection symmetry of the two-photon wave-packet function. More specifically, we propose precise control of the quantum coherence of two-photon pulses by engineering their transverse-plane phases. These results could potentially stimulate new experimental researches and applications of optical quantum coherence.

14.Collective Radiative Interactions in the Discrete Truncated Wigner Approximation

Authors:Christopher D. Mink, Michael Fleischhauer

Abstract: Interfaces of light and matter serve as a platform for exciting many-body physics and photonic quantum technologies. Due to the recent experimental realization of atomic arrays at sub-wavelength spacings, collective interaction effects such as superradiance have regained substantial interest. Their analytical and numerical treatment is however quite challenging. Here we develop a semiclassical approach to this problem that allows to describe the coherent and dissipative many-body dynamics of interacting spins while taking into account lowest-order quantum fluctuations. For this purpose we extend the discrete truncated Wigner approximation, originally developed for unitarily coupled spins, to include collective, dissipative spin processes by means of truncated correspondence rules. This maps the dynamics of the atomic ensemble onto a set of semiclassical, numerically inexpensive stochastic differential equations. We benchmark our method with exact results for the case of Dicke decay, which shows excellent agreement. We then study superradiance in a spatially extended three-dimensional, coherently driven gas and study the dynamics of atomic arrays coupled to the quantized radiation field. For small arrays we compare to exact simulations, again showing good agreement at early times and at moderate to strong driving.

15.Proof-of-work consensus by quantum sampling

Authors:Deepesh Singh, Boxiang Fu, Gopikrishnan Muraleedharan, Chen-Mou Cheng, Nicolas Roussy Newton, Peter P. Rohde, Gavin K. Brennen

Abstract: Since its advent in 2011, boson-sampling has been a preferred candidate for demonstrating quantum advantage because of its simplicity and near-term requirements compared to other quantum algorithms. We propose to use a variant, called coarse-grained boson-sampling (CGBS), as a quantum Proof-of-Work (PoW) scheme for blockchain consensus. The users perform boson-sampling using input states that depend on the current block information, and commit their samples to the network. Afterward, CGBS strategies are determined which can be used to both validate samples and to reward successful miners. By combining rewards to miners committing honest samples together with penalties to miners committing dishonest samples, a Nash equilibrium is found that incentivizes honest nodes. The scheme works for both Fock state boson sampling and Gaussian boson sampling and provides dramatic speedup and energy savings relative to computation by classical hardware.

16.Multi-qubit State Tomography with Few Pauli Measurements

Authors:Xudan Chai, Teng Ma, Qihao Guo, Zhangqi Yin, Hao Wu, Qing Zhao

Abstract: In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state tomography, reconstructs the density matrix of an unknown quantum state. Theoretically, reconstructing an unknown state using this method can be arbitrarily accurate. However, this is less practical owing to the huge burden of measurements and data processing for large numbers of qubits. Even comprising an efficient estimator and a precise algorithm, an optimal tomographic framework can also be overburdened owing to the exponential growth of the measurements. Moreover, the consequential postprocessing of huge amounts of data challenges the capacity of computers. Thus, it is crucial to build an efficient framework that requires fewer measurements but yields an expected accuracy. To this end, we built a tomography schema by which only a few Pauli measurements enable an accurate tomographic reconstruction. Subsequently, this schema was verified as efficient and accurate through numerical simulations on the tomography of multi-qubit quantum states. Furthermore, this schema was proven to be robust through numerical simulations on a noisy superconducting qubit system. Therefore, the tomography schema paves an alternatively effective way to reconstruct the density matrix of a quantum state owing to its efficiency and accuracy, which are essential for quantum state tomography.

17.Quantum Trajectory Approach to Error Mitigation

Authors:Brecht. I. C Donvil, Rochus Lechler, Joachim Ankerhold, Paolo Muratore-Ginanneschi

Abstract: Quantum Error Mitigation (EM) is a collection of strategies to reduce errors on noisy intermediate scale quantum (NISQ) devices on which proper quantum error correction is not feasible. One of such strategies aimed at mitigating noise effects of a known environment is to realise the inverse map of the noise using a set of completely positive maps weighted by a quasi-probability distribution, i.e. a probability distribution with positive and negative values. This quasi-probability distribution is realised using classical post-processing after final measurements of the desired observables have been made. Here we make a connection with quasi-probability EM and recent results from quantum trajectory theory for open quantum systems. We show that the inverse of noise maps can be realised by performing classical post-processing on the quantum trajectories generated by an additional reservoir with a quasi-probability measure called the influence martingale. We demonstrate our result on a model relevant for current NISQ devices. Finally, we show the quantum trajectories required for error correction can themselves be simulated by coupling an ancillary qubit to the system. In this way, we can avoid the introduction of the engineered reservoir.

18.Site Recurrence for continuous-time open quantum walks on the line

Authors:Newton Loebens

Abstract: In recent years, several properties and recurrence criteria of discrete-time open quantum walks (OQWs) have been presented. Recently, Pellegrini introduced continuous-time open quantum walks (CTOQWs) as continuous-time natural limits of discrete-time OQWs. In this work, we study semifinite CTOQWs and some of their basic properties concerning statistics, such as transition probabilities and site recurrence. The notion of SJK-recurrence for CTOQWs is introduced, and it is shown to be equivalent to the traditional concept of recurrence. This statistic arises from the definition of $\delta$-skeleton of CTOQWs, which is a dynamic that allows us to obtain a discrete-time OQW in terms of a CTOQW. We present a complete criterion for site recurrence in the case of CTOQW induced by a coin of finite dimension with a set of vertices $\mathbb{Z}$ such that its auxiliary Lindblad operator has a single stationary state. Finally, we present a similar criterion that completes the case in which the internal degree of freedom of each site is of dimension 2.

19.Probabilistic Interpolation of Quantum Rotation Angles

Authors:Bálint Koczor, John Morton, Simon Benjamin

Abstract: Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of $B$ bits of resolution, i.e. it might support only $2^B$ possible variants of a given physical gate. Naive discretization of an algorithm's gates to the nearest available options causes coherent errors, while decomposing an impermissible gate into several allowed operations increases circuit depth. Conversely, demanding higher $B$ can greatly complexify hardware. Here we explore an alternative: Probabilistic Angle Interpolation (PAI). This effectively implements any desired, continuously parametrised rotation by randomly choosing one of three discretised gate settings and postprocessing individual circuit outputs. The approach is particularity relevant for near-term applications where one would in any case average over many runs of circuit executions to estimate expected values. While PAI increases that sampling cost, we prove that the overhead is remarkably modest even with thousands of parametrised gates and only $7$ bits of resolution available. This is a profound relaxation of engineering requirements for first generation quantum computers. Moreover we conclude that, even for more mature late-NISQ hardware, a resolution of $9$--$10$ bits may suffice.

20.Neural Network Approach to the Simulation of Entangled States with One Bit of Communication

Authors:Peter Sidajaya, Aloysius Dewen Lim, Baichu Yu, Valerio Scarani

Abstract: Bell's theorem states that Local Hidden Variables (LHVs) cannot fully explain the statistics of measurements on some entangled quantum states. It is natural to ask how much supplementary classical communication would be needed to simulate them. We study two long-standing open questions in this field with neural network simulations and other tools. First, we present evidence that all projective measurements on partially entangled pure two-qubit states require only one bit of communication. We quantify the statistical distance between the exact quantum behaviour and the product of the trained network, or of a semianalytical model inspired by it. Second, while it is known on general grounds (and obvious) that one bit of communication cannot eventually reproduce all bipartite quantum correlation, explicit examples have proved evasive. Our search failed find one for several bipartite Bell scenarios with up to 5 inputs and 4 outputs, highlighting the power of one bit of communication in reproducing quantum correlations.

21.Ferrimagnetic Oscillator Magnetometer

Authors:John F. Barry, Reed A. Irion, Matthew H. Steinecker, Daniel K. Freeman, Jessica J. Kedziora, Reginald G. Wilcox, Danielle A. Braje

Abstract: Quantum sensors offer unparalleled precision, accuracy, and sensitivity for a variety of measurement applications. We report a compact magnetometer based on a ferrimagnetic sensing element in an oscillator architecture that circumvents challenges common to other quantum sensing approaches such as limited dynamic range, limited bandwidth, and dependence on vacuum, cryogenic, or laser components. The device exhibits a fixed, calibration-free response governed by the electron gyromagnetic ratio. Exchange narrowing in the ferrimagnetic material produces sub-MHz transition linewidths despite the high unpaired spin density ($\sim 10^{22}$ cm$^{-3}$). The magnetometer achieves a minimum sensitivity of 100 fT/$\sqrt{\text{Hz}}$ to AC magnetic fields of unknown phase and a sensitivity below 200 fT/$\sqrt{\text{Hz}}$ over a bandwidth $\gtrsim \! 1$ MHz. By encoding magnetic field in frequency rather than amplitude, the device provides a dynamic range in excess of 1 mT. The passive, thermal initialization of the sensor's quantum state requires only a magnetic bias field, greatly reducing power requirements compared to laser-initialized quantum sensors. With additional development, this device promises to be a leading candidate for high-performance magnetometry outside the laboratory, and the oscillator architecture is expected to provide advantages across a wide range of sensing platforms.

22.Optimizing rodeo projection

Authors:Thomas D. Cohen, Hyunwoo Oh

Abstract: The rodeo algorithm has been proposed recently as an efficient method in quantum computing for projection of a given initial state onto a state of fixed energy for systems with discrete spectra. In the initial formulation of the rodeo algorithm these times were chosen randomly via a Gaussian distribution with fixed RMS times. In this paper it is shown that such a random approach for choosing times suffers from exponentially large fluctuations in the suppression of unwanted components: as the number of iterations gets large, the distribution of suppression factors obtained from random selection approaches a log-normal distribution leading to remarkably large fluctuations. We note that by choosing times intentionally rather than randomly such fluctuations can be avoided and strict upper bounds on the suppression can be obtained. Moreover, the average suppression using fixed computational cost can be reduced by many orders of magnitude relative to the random algorithm. A key to doing this is to choose times that vary over exponentially many times scales, starting from a modest maximum scale and going down to time scales exponentially smaller.

23.Aging and Reliability of Quantum Networks

Authors:Lisa T. Weinbrenner, Lina Vandré, Tim Coopmans, Otfried Gühne

Abstract: Quantum information science may lead to technological breakthroughs in computing, cryptography and sensing. For the implementation of these tasks, however, complex devices with many components are needed and the quantum advantage may easily be spoiled by failure of few parts only. A paradigmatic example are quantum networks. There, not only noise sources like photon absorption or imperfect quantum memories lead to long waiting times and low fidelity, but also hardware components may break, leading to a dysfunctionality of the entire network. For the successful long-term deployment of quantum networks in the future, it is important to take such deterioration effects into consideration during the design phase. Using methods from reliability theory and the theory of aging we develop an analytical approach for characterizing the functionality of networks under aging and repair mechanisms, also for non-trivial topologies. Combined with numerical simulations, our results allow to optimize long-distance entanglement distribution under aging effects.

24.Non-stabilizerness and entanglement from cat-state injection

Authors:Filipa C. R. Peres, Rafael Wagner, Ernesto F. Galvão

Abstract: Recently, cat states have been used to heuristically improve the runtime of a classical simulator of quantum circuits based on the diagrammatic ZX-calculus. Here we explore the use of cat-state injection within the quantum circuit model. We introduce a new family of cat states $\left| \mathrm{cat}_m^* \right>$, and describe circuit gadgets using them to concurrently inject non-stabilizerness (also known as magic) and entanglement into any quantum circuit. We provide numerical evidence that cat-state injection does not lead to speed-up in classical simulation. On the other hand, we show that our gadgets can be used to widen the scope of compelling applications of cat states. Specifically, we show how to leverage them to achieve savings in the number of injected qubits, and also to induce scrambling dynamics in otherwise non-entangling Clifford circuits in a controlled manner.

25.Software Architecture for Operation and Use of Quantum Communications Networks

Authors:Dinesh Verma, Eden Figueroa, Gabriella Carini, Mark Ritter

Abstract: Quantum Communications Networks using the properties of qubits, namely state superposition, no-cloning and entanglement, can enable the exchange of information in a very secure manner across optical links or free space. New innovations enable the use of optical repeaters as well as multi-cast communication in the networks. Some types of quantum communications mechanisms can be implemented at room-temperature instead of requiring super-cooled systems. This makes it likely that business impact from quantum communications will be realized sooner than that from quantum computers. Quantum networks need to be integrated into the ecosystem of currently deployed classical networks and augment them with new capabilities. Classical computers and networks need to be able to use the new secure communication capabilities offered by quantum networks. To provide this interoperability, appropriate software abstractions on the usage of quantum networks need to be developed. In this paper, we examine what the type of software abstractions quantum networks can provide, and the type of applications that the new abstractions can support.

26.Controlling the Photon Number Coherence of Solid-state Quantum Light Sources for Quantum Cryptography

Authors:Yusuf Karli, Daniel A. Vajner, Florian Kappe, Paul C. A. Hagen, Lena M. Hansen, René Schwarz, Thomas K. Bracht, Christian Schimpf, Saimon F. Covre da Silva, Philip Walther, Armando Rastelli, Vollrath Martin Axt, Juan C. Loredo, Vikas Remesh, Tobias Heindel, Doris E. Reiter, Gregor Weihs

Abstract: Quantum communication networks rely on quantum cryptographic protocols including quantum key distribution (QKD) using single photons. A critical element regarding the security of QKD protocols is the photon number coherence (PNC), i.e. the phase relation between the zero and one-photon Fock state, which critically depends on the excitation scheme. Thus, to obtain flying qubits with the desired properties, optimal pumping schemes for quantum emitters need to be selected. Semiconductor quantum dots generate on-demand single photons with high purity and indistinguishability. Exploiting two-photon excitation of a quantum dot combined with a stimulation pulse, we demonstrate the generation of high-quality single photons with a controllable degree of PNC. Our approach provides a viable route toward secure communication in quantum networks.

27.Spin squeezing in internal bosonic Josephson junctions via enhanced shortcuts to adiabaticity

Authors:Manuel Odelli, Vladimir M. Stojanovic, Andreas Ruschhaupt

Abstract: We investigate a time-efficient and robust preparation of spin-squeezed states -- a class of states of interest for quantum-enhanced metrology -- in internal bosonic Josephson junctions with a time-dependent interaction strength between atoms in two different hyperfine states. We treat this state-preparation problem, which had previously been addressed using shortcuts to adiabaticity (STA), using the recently proposed analytical modification of this class of quantum-control protocols that became known as the enhanced STA (eSTA) method. We characterize the state-preparation process by evaluating the time dependence of the coherent spin-squeezing and number-squeezing parameters and the target-state fidelity. We show that the state-preparation times obtained using the eSTA method compare favourably to those found in previously proposed approaches. Even more importantly, we demonstrate that the increased robustness of the eSTA approach -- compared to its STA counterpart -- leads to additional advantages for potential experimental realizations of strongly spin-squeezed states.

28.On the Origin of Linearity and Unitarity in Quantum Theory

Authors:Matt Wilson, Nick Ormrod

Abstract: We reconstruct the transformations of quantum theory using a physically motivated postulate. This postulate states that transformations should be locally applicable, and singles out the linear unitary maps of pure quantum theory, as well as the completely positive, trace-preserving maps of mixed quantum theory. Notably, in the pure case, linearity with respect to the superposition rule on Hilbert spaces is derived rather than assumed (and without any continuity assumptions).

29.A survey on the complexity of learning quantum states

Authors:Anurag Anshu, Srinivasan Arunachalam

Abstract: We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical functions encoded as quantum states. We highlight how these results are paving the way for a highly successful theory with a range of exciting open questions. To this end, we distill 25 open questions from these results.

30.Probing post-measurement entanglement without post-selection

Authors:Samuel J. Garratt, Ehud Altman

Abstract: We study the problem of observing quantum collective phenomena emerging from large numbers of measurements. These phenomena are difficult to observe in conventional experiments because, in order to distinguish the effects of measurement from dephasing, it is necessary to post-select on sets of measurement outcomes whose Born probabilities are exponentially small in the number of measurements performed. An unconventional approach, which avoids this exponential `post-selection problem', is to construct cross-correlations between experimental data and the results of simulations on classical computers. However, these cross-correlations generally have no definite relation to physical quantities. We first show how to incorporate shadow tomography into this framework, thereby allowing for the construction of quantum information-theoretic cross-correlations. We then identify cross-correlations which both upper and lower bound the measurement-averaged von Neumann entanglement entropy. These bounds show that experiments can be performed to constrain post-measurement entanglement without the need for post-selection. To illustrate our technique we consider how it could be used to observe the measurement-induced entanglement transition in Haar-random quantum circuits. We use exact numerical calculations as proxies for quantum simulations and, to highlight the fundamental limitations of classical memory, we construct cross-correlations with tensor-network calculations at finite bond dimension. Our results reveal a signature of measurement-induced criticality that can be observed using a quantum simulator in polynomial time and with polynomial classical memory.

1.Energy-time Entanglement Coexisting with Fiber Optical Communication at Telecom C-band

Authors:Yun-Ru Fan, Yue Luo, Zi-Chang Zhang, Yun-Bo Li, Sheng Liu, Dong Wang, Dechao Zhang, Guang-Wei Deng, You Wang, Hai-Zhi Song, Zhen Wang, Li-Xing You, Chen-Zhi Yuan, Guang-Can Guo, Qiang Zhou

Abstract: The coexistence of quantum and classical light in the same fiber link is extremely desired in developing quantum communication. It has been implemented for different quantum information tasks, such as classical light coexisting with polarization-entangled photons at telecom O-band, and with quantum signal based quantum key distribution (QKD). In this work, we demonstrate the coexistence of energy-time entanglement based QKD and fiber optical communication at the telecom C-band. The property of noise from the classical channel is characterized with classical light at different wavelengths. With the largest noise, i.e., the worst case, the properties of energy-time entanglement are measured at different fiber optical communication rates. By measuring the two-photon interference of energy-time entanglement, our results show that a visibility of 82.01$\pm$1.10\% is achieved with a bidirectional 20 Gbps fiber optical communication over 40 km. Furthermore, by performing the BBM92 protocol for QKD, a secret key rate of 245 bits per second could be generated with a quantum bit error rate of 8.88\% with the coexisted energy-time entanglement.~Our demonstration paves the way for developing the infrastructure for quantum networks compatible with fiber optical communication.

2.Phase Correction using Deep Learning for Satellite-to-Ground CV-QKD

Authors:Nathan K. Long, Robert Malaney, Kenneth J. Grant

Abstract: Coherent measurement of quantum signals used for continuous-variable (CV) quantum key distribution (QKD) across satellite-to-ground channels requires compensation of phase wavefront distortions caused by atmospheric turbulence. One compensation technique involves multiplexing classical reference pulses (RPs) and the quantum signal, with direct phase measurements on the RPs then used to modulate a real local oscillator (RLO) on the ground - a solution that also removes some known attacks on CV-QKD. However, this is a cumbersome task in practice - requiring substantial complexity in equipment requirements and deployment. As an alternative to this traditional practice, here we introduce a new method for estimating phase corrections for an RLO by using only intensity measurements from RPs as input to a convolutional neural network, mitigating completely the necessity to measure phase wavefronts directly. Conventional wisdom dictates such an approach would likely be fruitless. However, we show that the phase correction accuracy needed to provide for non-zero secure key rates through satellite-to-ground channels is achieved by our intensity-only measurements. Our work shows, for the first time, how artificial intelligence algorithms can replace phase-measuring equipment in the context of CV-QKD delivered from space, thereby delivering an alternate deployment paradigm for this global quantum-communication application.

3.Optimal Lossless Dynamic Quantum Huffman Block Encoding

Authors:George Androulakis, Rabins Wosti

Abstract: In this article we present an adaptation of the quantum Huffman encoding which was introduced in [IEEE Transactions on information theory 46.4 (2000): 1644-1649] and was studied in [Scientific Reports 7.1 (2017): 14765]. Our adaptation gives a block encoding as it is applied successively to encode one block after the other. It is also a dynamic encoding because it is updated at every block. We prove that our encoding gives the optimal average codeword length over any other dynamic block encoding with a common jointly orthonormal sequence of length codewords.

4.Variational Quantum Algorithm based circuit that implements the Toffoli gate with multi inputs

Authors:Yuval Idan, M. N. Jayakody

Abstract: The prime objective of this study is to seek a circuit diagram for a multi-inputs Toffoli gate including only single qubit gates and CNOTs. In this regard, we have developed two variational quantum algorithms that can be used to implement a multi-inputs Toffoli gate. The cost functions of these two VQAs are derived by using the Hilbert Schmidt inner product and the expected value of an observable that can capture the difference between the inputs and outputs of a Toffoli gate. We employ two ansatz circuit architectures and use the PennyLane package to execute the optimization.

5.Improving Performance in Combinatorial Optimization Problems with Inequality Constraints: An Evaluation of the Unbalanced Penalization Method on D-Wave Advantage

Authors:J. A. Montanez-Barrera, Pim van den Heuvel, Dennis Willsch, Kristel Michielsen

Abstract: Combinatorial optimization problems are one of the target applications of current quantum technology, mainly because of their industrial relevance, the difficulty of solving large instances of them classically, and their equivalence to Ising Hamiltonians using the quadratic unconstrained binary optimization (QUBO) formulation. Many of these applications have inequality constraints, usually encoded as penalization terms in the QUBO formulation using additional variables known as slack variables. The slack variables have two disadvantages: (i) these variables extend the search space of optimal and suboptimal solutions, and (ii) the variables add extra qubits and connections to the quantum algorithm. Recently, a new method known as unbalanced penalization has been presented to avoid using slack variables. This method offers a trade-off between additional slack variables to ensure that the optimal solution is given by the ground state of the Ising Hamiltonian, and using an unbalanced heuristic function to penalize the region where the inequality constraint is violated with the only certainty that the optimal solution will be in the vicinity of the ground state. This work tests the unbalanced penalization method using real quantum hardware on D-Wave Advantage for the traveling salesman problem (TSP). The results show that the unbalanced penalization method outperforms the solutions found using slack variables and sets a new record for the largest TSP solved with quantum technology.

6.Dynamic resonance fluorescence in solid-state cavity quantum electrodynamics

Authors:Shunfa Liu, Chris Gustin, Hanqing Liu, Xueshi Li, Ying Yu, Haiqiao Ni, Zhichuan Niu, Stephen Hughes, Xuehua Wang, Jin Liu

Abstract: The coherent interaction between a two-level system and electromagnetic fields serves as a foundation for fundamental quantum physics and modern photonic quantum technology. A profound example is resonance fluorescence, where the non-classical photon emission appears in the form of a Mollow-triplet when a two-level system is continuously driven by a resonant laser. Pushing resonance fluorescence from a static to dynamic regime by using short optical pulses generates on-demand emissions of highly coherent single photons. Further increasing the driving strength in the dynamical regime enables the pursuit of exotic non-classical light emission in photon number superposition, photon number entanglement, and photon bundle states. However, the long-sought-after spectrum beyond the Mollow-triplet, a characteristic of dynamic resonance fluorescence under strong driving strength, has not been observed yet. Here we report the direct observation and systematic investigations of dynamic resonance fluorescence spectra beyond the Mollow-triplet in a solid-state cavity quantum electrodynamic system. The dynamic resonance fluorescence spectra with up to five pairs of side peaks, excitation detuning induced spectral asymmetry, and cavity filtering effect are observed and quantitatively modeled by a full quantum model with phonon scattering included. Time-resolved measurements further reveal that the multiple side peaks originate from interference of the emission associated with different temporal positions of the excitation pulses. Our work facilitates the generation of a variety of exotic quantum states of light with dynamic driving of two-level systems.

7.Instability of multi-mode systems with quadratic Hamiltonians

Authors:Xuanloc Leu, Xuan-Hoai Thi Nguyen, Jinhyoung Lee

Abstract: We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric perspective of instability: A quantum quadratic system is dynamically unstable if and only if its Hamiltonian is hyperbolic. By applying our geometric method, we analyze the stability of two-mode and three-mode optomechanical systems. Remarkably, our approach demonstrates that these systems can be stabilized over a wider range of system parameters compared to the conventional rotating wave approximation (RWA) assumption. Furthermore, we reveal that the systems transit their phases from stable to unstable, when the system parameters cross specific critical boundaries. The results imply the presence of multistability in the optomechanical systems.

8.Altering level shifts and spontaneous decay rates of distant atoms \\ using partially-transparent asymmetric mirror interfaces

Authors:Nicholas Furtak-Wells, Benjamin Dawson, Thomas Mann, Gin Jose, Almut Beige

Abstract: In three dimensions, dipole-dipole interactions which alter atomic level shifts and spontaneous decay rates only persist over distances comparable to the wavelength of the emitted light. To provide novel tools for quantum technology applications, like quantum sensing, many attempts have been made to extend the range of these interactions. In this paper we show that this can be achieved with the help of partially-transparent asymmetric interfaces {\em without} involving negative index metamaterials. Suppose two atoms are placed on opposite sides of the interface, each at the position of the mirror image of the other. In this case, their emitted light interferes exactly as it would when the atoms are right next to each~other. Hence their dipole-dipole interaction assumes an additional maximum, even when the actual distance of the atoms is several orders of magnitude larger than their transition wavelength.

9.A telecom band single-photon source using a grafted carbon nanotube coupled to a fiber Fabry-Perot cavity in the Purcell regime

Authors:Antoine Borel, Théo Habrant-Claude, Federico Rapisarda, Jakob Reichel, Steeve Doorn, Christophe Voisin, Yannick Chassagneux

Abstract: We report on the coupling of a reconfigurable high Q fiber micro-cavity to an organic color center grafted to a carbon nanotube for telecom wavelength emission of single photons in the Purcell regime. Using three complementary approaches we assess various figures of merit of this tunable single photon source and of the cavity quantum electrodynamical effects : the brightening of the emitter is obtained by comparison of the count rates of the very same emitter in free-space and cavity coupled regimes. We demonstrate a fiber coupled single-photon output rate up to 20 MHz at 1275~nm. Using time-resolved and saturation measurements, we determine independently the radiative quantum yield and the Purcell factor of the system with values up to 30 for the smallest mode volumes. Finally, we take advantage of the tuning capability of the cavity to measure the spectral profile of the brightness of the source which gives access to the vacuum Rabi splitting $g$ with values up to $25 \; \mu$eV.

10.Identifying quantum change points for Hamiltonians

Authors:Kenji Nakahira

Abstract: The identification of environmental changes is crucial in many fields. The present research is aimed at investigating the optimal performance for detecting change points in a quantum system when its Hamiltonian suddenly changes at a specific time. Assume that the Hamiltonians before and after the change are known and that the prior probability of each prospective change point is identical. These Hamiltonians can be time-dependent. The problem considered in this study is an extension of the problem of discriminating multiple quantum processes that consist of sequences of quantum channels. Although it is often extremely difficult to find an analytical solution to such a problem, we demonstrate that the maximum success probability for the Hamiltonian change point problem can be determined analytically and has a simple form.

11.Long-distance measurement-device-independent quantum key distribution using entangled states between continuous and discrete variables

Authors:Soumyakanti Bose, Jaskaran Singh, Adán Cabello, Hyunseok Jeong

Abstract: We introduce a feasible scheme to produce high-rate long-distance entanglement which uses hybrid entanglement (HE) between continuous variables (CV) and discrete variables (DV). We show that HE can effectively remove the experimental limitations of existing CV and DV measurement-device-independent quantum key distribution (MDI-QKD) protocols. The key idea is using the CV part, which can be adjusted to be robust against photon losses, for increasing the transmission distance, while using the DV part for achieving high secure key rates. We show that, using HE states, MDI-QKD is possible with standard telecom fibers for 300 km with a secure key rate which is an order of magnitude higher than in existing protocols. Our results point out that HE states provide advantage for practical long-distance high-rate entanglement.

12.A diamond nanophotonic interface with an optically accessible deterministic electronuclear spin register

Authors:Ryan A. Parker, Jesús Arjona Martínez, Kevin C. Chen, Alexander M. Stramma, Isaac B. Harris, Cathryn P. Michaels, Matthew E. Trusheim, Martin Hayhurst Appel, Carola M. Purser, William G. Roth, Dirk Englund, Mete Atatüre

Abstract: A contemporary challenge for the scalability of quantum networks is developing quantum nodes with simultaneous high photonic efficiency and long-lived qubits. Here, we present a fibre-packaged nanophotonic diamond waveguide hosting a tin-vacancy centre with a spin-1/2 $^{117}$Sn nucleus. The interaction between the electronic and nuclear spins results in a signature 452(7) MHz hyperfine splitting. This exceeds the natural optical linewidth by a factor of 16, enabling direct optical nuclear-spin initialisation with 98.6(3)% fidelity and single-shot readout with 80(1)% fidelity. The waveguide-to-fibre extraction efficiency of our device of 57(6)% enables the practical detection of 5-photon events. Combining the photonic performance with the optically initialised nuclear spin, we demonstrate a spin-gated single-photon nonlinearity with 11(1)% contrast in the absence of an external magnetic field. These capabilities position our nanophotonic interface as a versatile quantum node in the pursuit of scalable quantum networks.

13.Quantum Convolutional Neural Networks for Multi-Channel Supervised Learning

Authors:Anthony M. Smaldone, Gregory W. Kyro, Victor S. Batista

Abstract: As the rapidly evolving field of machine learning continues to produce incredibly useful tools and models, the potential for quantum computing to provide speed up for machine learning algorithms is becoming increasingly desirable. In particular, quantum circuits in place of classical convolutional filters for image detection-based tasks are being investigated for the ability to exploit quantum advantage. However, these attempts, referred to as quantum convolutional neural networks (QCNNs), lack the ability to efficiently process data with multiple channels and therefore are limited to relatively simple inputs. In this work, we present a variety of hardware-adaptable quantum circuit ansatzes for use as convolutional kernels, and demonstrate that the quantum neural networks we report outperform existing QCNNs on classification tasks involving multi-channel data. We envision that the ability of these implementations to effectively learn inter-channel information will allow quantum machine learning methods to operate with more complex data. This work is available as open source at

14.Multipartite entanglement theory with entanglement-nonincreasing operations

Authors:Alexander Streltsov

Abstract: A key problem in quantum information science is to determine optimal protocols for the interconversion of entangled states shared between remote parties. While for two parties a large number of results in this direction is available, the multipartite setting still remains a major challenge. In this Letter, this problem is addressed by extending the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. Specifically, we consider transformations capable of introducing a small, controllable increase of entanglement of a state, with the requirement that the increase can be made arbitrarily small. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states. Remarkably, this approach allows the reduction of tripartite entanglement to its bipartite analog, indicating that every pure tripartite state can be reversibly synthesized from a suitable number of singlets distributed between pairs of parties.

15.Implementing Jastrow--Gutzwiller operators on a quantum computer using the cascaded variational quantum eigensolver algorithm

Authors:John P. T. Stenger, C. Stephen Hellberg, Daniel Gunlycke

Abstract: A Jastrow--Gutzwiller operator adds many-body correlations to a quantum state. However, the operator is non-unitary, making it difficult to implement directly on a quantum computer. We present a novel implementation of the Jastrow--Gutzwiller operator using the cascaded variational quantum eigensolver algorithm. We demonstrate the method on IBM Q Lagos for a Hubbard model.

16.Parity-time-symmetric two-qubit system: entanglement and sensing

Authors:J. Zhang, Y. L. Zhou, Y. L. Zuo, P. X. Chen, H. Jing, L. M. Kuang

Abstract: In this paper we study exceptional-point (EP) effects and quantum sensing in a parity-time (PT)-symmetric two-qubit system with the Ising-type interaction. We explore EP properties of the system by analyzing degeneracy of energy eigenvalues or entanglement of eigenstates. We investigate entanglement dynamics of the two qubits in detail. In particular, we demonstrate that the system can create the steady-state entanglement in the PT-broken phase and collapse-revival phenomenon of entanglement in the PT-symmetric phase during the long-time evolution. We show that entanglement can be generated more quickly than the corresponding Hermitian system. Finally, we prove that the sensitivity of eigenstate quantum sensing for the parameters exhibits the remarkable enharncement at EPs, and propose a quantum-coherence measurement to witness the existence of EPs.

17.Quantum propagator for a general time-dependent quadratic Hamiltonian: Application to interacting oscillators in external fields

Authors:Shohreh Janjan, Fardin Kheirandish

Abstract: In this paper, we find the quantum propagator for a general time-dependent quadratic Hamiltonian. The method is based on the properties of the propagator and the fact that the quantum propagator fulfills two independent partial differential equations originating from Heisenberg equations for positions and momenta. As an application of the method, we find the quantum propagator for a linear chain of interacting oscillators for both periodic and Dirichlet boundary conditions. The state and excitation propagation along the harmonic chain in the absence and presence of an external classical source is studied and discussed. The location of the first maxima of the probability amplitude $P(n,\tau)$ is a straight line in the $(n,\tau)$-plane, indicating a constant speed of excitation propagation along the chain.

18.Amplified Nanoscale Detection of Labelled Molecules via Surface Electrons on Diamond

Authors:A. Biteri-Uribarren, P. Alsina-Bolívar, C. Munuera-Javaloy, R. Puebla, J. Casanova

Abstract: The detection of individual molecules and their dynamics has been a long-standing challenge in the field of nanotechnology. In this work, we present a method that utilizes a nitrogen vacancy (NV) center and a dangling-bond on the diamond surface to measure the coupling between two electronic targets tagged on a macromolecule. To achieve this, we design a multi-tone dynamical decoupling sequence that leverages the strong interaction between the nitrogen vacancy center and the dangling bond. In addition, this sequence minimizes the impact of decoherence finally resulting in an increased signal-to-noise ratio. This proposal has the potential to open up new avenues for fundamental research and technological innovation in distinct areas such as biophysics and biochemistry.

19.Mid-circuit qubit measurement and rearrangement in a $^{171}$Yb atomic array

Authors:M. A. Norcia, W. B. Cairncross, K. Barnes, P. Battaglino, A. Brown, M. O. Brown, K. Cassella, C. -A. Chen, R. Coxe, D. Crow, J. Epstein, C. Griger, A. M. W. Jones, H. Kim, J. M. Kindem, J. King, S. S. Kondov, K. Kotru, J. Lauigan, M. Li, M. Lu, E. Megidish, J. Marjanovic, M. McDonald, T. Mittiga, J. A. Muniz, S. Narayanaswami, C. Nishiguchi, R. Notermans, T. Paule, K. Pawlak, L. Peng, A. Ryou, A. Smull, D. Stack, M. Stone, A. Sucich, M. Urbanek, R. van de Veerdonk, Z. Vendeiro, T. Wilkason, T. -Y. Wu, X. Xie, B. J. Bloom

Abstract: Measurement-based quantum error correction relies on the ability to determine the state of a subset of qubits (ancillae) within a processor without revealing or disturbing the state of the remaining qubits. Among neutral-atom based platforms, a scalable, high-fidelity approach to mid-circuit measurement that retains the ancilla qubits in a state suitable for future operations has not yet been demonstrated. In this work, we perform imaging using a narrow-linewidth transition in an array of tweezer-confined $^{171}$Yb atoms to demonstrate nondestructive state-selective and site-selective detection. By applying site-specific light shifts, selected atoms within the array can be hidden from imaging light, which allows a subset of qubits to be measured while causing only percent-level errors on the remaining qubits. As a proof-of-principle demonstration of conditional operations based on the results of the mid-circuit measurements, and of our ability to reuse ancilla qubits, we perform conditional refilling of ancilla sites to correct for occasional atom loss, while maintaining the coherence of data qubits. Looking towards true continuous operation, we demonstrate loading of a magneto-optical trap with a minimal degree of qubit decoherence.

20.Efficient stabilizer entropies for quantum computers

Authors:Tobias Haug, Soovin Lee, M. S. Kim

Abstract: Stabilizer entropies (SEs) are measures of nonstabilizerness or `magic' that quantify the degree to which a state is described by stabilizers. SEs are especially interesting due to their connections to scrambling, localization and property testing. However, practical applications have been limited so far as previously known measurement protocols for SEs scale exponentially with the number of qubits. Here, we introduce the Tsallis-$n$ SE as an efficient measure of nonstabilizerness for quantum computers. We find that the number of measurements is independent of the number of qubits for any integer index $n>1$ which ensures the scalability of the measure. The Tsallis SE is an efficient bound of various nonstabilizerness monotones which are intractable to compute beyond a few qubits. Using the IonQ quantum computer, we experimentally measure the Tsallis SE of random Clifford circuits doped with non-Clifford gates and give bounds for the stabilizer fidelity, stabilizer extent and robustness of magic. As applications, we provide efficient algorithms to measure $4n$-point out-of-time-order correlators and multifractal flatness. Our results open up the exploration of nonstabilizerness with quantum computers.

21.Lamb shift as a witness for quantum noninertial effects

Authors:Navdeep Arya

Abstract: The sustained intense experimental activity around atomic spectroscopy and the resulting high-precision measurements of atomic spectral lines attract interest in Lamb shift as a witness for noninertial effects in quantum systems. We investigate the Lamb shift in a two-level system undergoing uniform circular motion and coupled to a quantum electromagnetic field inside a cavity. We show that when the separation between different cavity modes is large compared to the width of each cavity mode, both the inertial and noninertial contributions to the Lamb shift are convergent. In addition, we find that the purely-noninertial Lamb shift maximizes away from the atomic resonance by an amount decided by the angular frequency of the circulating atom, lending itself to efficient enhancement by a suitable tuning of the cavity parameters. We argue that the noninertial contribution becomes detectable at accelerations $\sim 10^{14}~\mathrm{m/s^2}$.

22.Witnessing environment dimension through temporal correlations

Authors:Lucas B. Vieira, Simon Milz, Giuseppe Vitagliano, Costantino Budroni

Abstract: We introduce a framework to compute upper bounds for temporal correlations achievable in open quantum system dynamics, obtained by repeated measurements on the system. As these correlations arise by virtue of the environment acting as a memory resource, such bounds are witnesses for the minimal dimension of an effective environment compatible with the observed statistics. These witnesses are derived from a hierarchy of semidefinite programs with guaranteed asymptotic convergence. We compute non-trivial bounds for various sequences involving a qubit system and a qubit environment, and compare the results to the best known quantum strategies producing the same outcome sequences. Our results provide a numerically tractable method to determine bounds on multi-time probability distributions in open quantum system dynamics and allow for the witnessing of effective environment dimensions through probing of the system alone.

23.Hybrid variational quantum eigensolvers: merging computational models

Authors:Albie Chan, Zheng Shi, Luca Dellantonio, Wolfgang Dür, Christine A. Muschik

Abstract: Variational quantum eigensolvers (VQEs) are a highly successful technique for simulating physical models on quantum computers. Recently, they were extended to the measurement-based approach of quantum computing, bringing the strengths and advantages of this computational model to VQEs. In this work, we push the design and integration frontiers of VQE further by blending measurement-based elements into the gate-based paradigm to form a hybrid VQE. This facilitates the design of a problem-informed variational ansatz and also allows the efficient implementation of many-body Hamiltonians on NISQ devices. We experimentally demonstrate our approach on a superconducting quantum computer by investigating the perturbed planar code, Z2 and SU(3) lattice gauge theories, and the LiH molecule.

24.Universal Quantum Computation in Globally Driven Rydberg Atom Arrays

Authors:Francesco Cesa, Hannes Pichler

Abstract: We develop a model for quantum computation which only relies on global driving, without the need of local addressing of the qubits. Our scheme is based on dual-species processors, and we present it in the framework on neutral atoms subjected to Rydberg blockade constraints. A circuit is imprinted in the (static) trap positions of the atoms, and the algorithm is executed by a sequence of global, resonant laser pulses; we show that this model for quantum computation is universal and scalable.

25.Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation

Authors:Baptiste Anselme Martin, Thomas Ayral, François Jamet, Marko J. Rančić, Pascal Simon

Abstract: Matrix Product States (MPS) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the entanglement entropy. While MPS can efficiently find ground states of 1D systems, their capacities are limited when simulating their dynamics, where the entanglement can increase ballistically with time. On the other hand, quantum devices appear as a natural platform to encode correlated many-body states, suited to perform time evolution. However, accessing the regime of modeling long-time dynamics is hampered by quantum noise. In this study we use the best of worlds: the short-time dynamics is efficiently performed by MPSs, compiled into short-depth quantum circuits followed by Trotter circuits run on a quantum computer. We quantify the capacities of this hybrid classical-quantum scheme in terms of fidelities and entanglement production taking into account a realistic noise model. We show that using classical knowledge in the form of MPSs provides a way to better use limited quantum resources and lowers the noise requirements to reach a practical quantum advantage. Combined with powerful noise-mitigation methods our approach allows us to simulate an 8-qubit system on an actual quantum device over a longer time scale than low bond dimension MPSs and purely quantum Trotter evolution.

26.The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios

Authors:Lucas E. A. Porto, Rafael Rabelo, Marcelo Terra Cunha, Adán Cabello

Abstract: A necessary condition for the probabilities of a set of events to exhibit Bell nonlocality or Kochen-Specker contextuality is that the graph of exclusivity of the events contains induced odd cycles with five or more vertices, called odd holes, or their complements, called odd antiholes. From this perspective, events whose graph of exclusivity are odd holes or antiholes are the building blocks of contextuality. For any odd hole or antihole, any assignment of probabilities allowed by quantum mechanics can be achieved in specific contextuality scenarios. However, here we prove that, for any odd hole, the probabilities that attain the quantum maxima cannot be achieved in Bell scenarios. We also prove it for the simplest odd antiholes. This leads us to the conjecture that the quantum maxima for any of the building blocks cannot be achieved in Bell scenarios. This result sheds light on why the problem of whether a probability assignment is quantum is decidable, while whether a probability assignment within a given Bell scenario is quantum is, in general, undecidable. This also helps to undertand why identifying principles for quantum correlations is simpler when we start by identifying principles for quantum sets of probabilities defined with no reference to specific scenarios.

27.Mid-circuit operations using the omg-architecture in neutral atom arrays

Authors:Joanna W. Lis, Aruku Senoo, William F. McGrew, Felix Rönchen, Alec Jenkins, Adam M. Kaufman

Abstract: We implement mid-circuit operations in a 48-site array of neutral atoms, enabled by new methods for control of the $\textit{omg}$ (optical-metastable-ground state qubit) architecture present in ${}^{171}$Yb. We demonstrate laser-based control of ground, metastable and optical qubits with average single-qubit fidelities of $F_{g} = 99.968(3)$, $F_{m} = 99.12(4)$ and $F_{o} = 99.804(8)$. With state-sensitive shelving between the ground and metastable states, we realize a non-destructive state-detection for $^{171}$Yb, and reinitialize in the ground state with either global control or local feed-forward operations. We use local addressing of the optical clock transition to perform mid-circuit operations, including measurement, spin reset, and motional reset in the form of ground-state cooling. In characterizing mid-circuit measurement on ground-state qubits, we observe raw errors of $1.8(6)\%$ on ancilla qubits and $4.5(1.0)\%$ on data qubits, with the former (latter) uncorrected for $1.0(2)\%$ ($2.0(2)\%$) preparation and measurement error; we observe similar performance for mid-circuit reset operations. The reported realization of the $\textit{omg}$ architecture and mid-circuit operations are door-opening for many tasks in quantum information science, including quantum error-correction, entanglement generation, and metrology.

1.Comprehensive scheme for identifying defects in solid-state quantum systems

Authors:Chanaprom Cholsuk, Sujin Suwanna, Tobias Vogl

Abstract: A solid-state quantum emitter is one of the indispensable components for optical quantum technologies. Ideally, an emitter should have a compatible wavelength for efficient coupling to other components in a quantum network. It is therefore essential to understand fluorescent defects that lead to specific emitters. In this work, we employ density functional theory (DFT) to demonstrate the calculation of the complete optical fingerprints of quantum emitters in the two-dimensional material hexagonal boron nitride. These emitters are of great interest, yet many of them are still to be identified. Our results suggest that instead of comparing a single optical property, such as the commonly used zero-phonon line energy, multiple properties should be used when comparing theoretical simulations to the experiment. This way, the entire electronic structure can be predicted and quantum emitters can be designed and tailored. Moreover, we apply this approach to predict the suitability for using the emitters in specific quantum applications, demonstrating through the examples of the Al$_{\text{N}}$ and P$_{\text{N}}$V$_{\text{B}}$ defects. We therefore combine and apply DFT calculations to identify quantum emitters in solid-state crystals with a lower risk of misassignments as well as a way to design and tailor optical quantum systems. This consequently serves as a recipe for classification and the generation of universal solid-state quantum emitter systems in future hybrid quantum networks.

2.Quafu-RL: The Cloud Quantum Computers based Quantum Reinforcement Learning

Authors:BAQIS Quafu Group

Abstract: With the rapid advent of quantum computing, hybrid quantum-classical machine learning has shown promising computational advantages in many key fields. Quantum reinforcement learning, as one of the most challenging tasks, has recently demonstrated its ability to solve standard benchmark environments with formally provable theoretical advantages over classical counterparts. However, despite the progress of quantum processors and the emergence of quantum computing clouds in the noisy intermediate-scale quantum (NISQ) era, algorithms based on parameterized quantum circuits (PQCs) are rarely conducted on NISQ devices. In this work, we take the first step towards executing benchmark quantum reinforcement problems on various real devices equipped with at most 136 qubits on BAQIS Quafu quantum computing cloud. The experimental results demonstrate that the Reinforcement Learning (RL) agents are capable of achieving goals that are slightly relaxed both during the training and inference stages. Moreover, we meticulously design hardware-efficient PQC architectures in the quantum model using a multi-objective evolutionary algorithm and develop a learning algorithm that is adaptable to Quafu. We hope that the Quafu-RL be a guiding example to show how to realize machine learning task by taking advantage of quantum computers on the quantum cloud platform.

3.Tristochastic operations and convolutions of quantum states

Authors:Rafał Bistroń, Wojciech Śmiałek, Karol Życzkowski

Abstract: The notion of convolution of two probability vectors, corresponding to a coincidence experiment can be extended for a family of binary operations determined by (tri)stochastic tensors, to describe Markov chains of a higher order. The problem of associativity, commutativity and the existence of neutral elements and inverses is analyzed for such operations. For a more general setup of multi-stochastic tensors, we present the characterization of their probability eigenvectors. Similar results are obtained for the quantum case: we analyze tristochastic channels, which induce binary operations defined in the space of quantum states. Studying coherifications of tristochastic tensors we propose a quantum analogue of the convolution of probability vectors defined for two arbitrary density matrices of the same size. Possible applications of this notion to construct schemes of error mitigation or building blocks in quantum convolutional neural networks are discussed.

4.Quafu-Qcover: Explore Combinatorial Optimization Problems on Cloud-based Quantum Computers

Authors:BAQIS Quafu Group

Abstract: We present Quafu-Qcover, an open-source cloud-based software package designed for combinatorial optimization problems that support both quantum simulators and hardware backends. Quafu-Qcover provides a standardized and complete workflow for solving combinatorial optimization problems using the Quantum Approximate Optimization Algorithm (QAOA). It enables the automatic modeling of the original problem as a quadratic unconstrained binary optimization (QUBO) model and corresponding Ising model, which can be further transformed into a weight graph. The core of Qcover relies on a graph decomposition-based classical algorithm, which enables obtaining the optimal parameters for the shallow QAOA circuit more efficiently. Quafu-Qcover includes a specialized compiler that translates QAOA circuits into physical quantum circuits capable of execution on Quafu cloud quantum computers. Compared to a general-purpose compiler, ours generates shorter circuit depths while also possessing better speed performance. The Qcover compiler can establish a library of qubits coupling substructures in real time based on the updated calibration data of the superconducting quantum devices, ensuring that the task is executed on physical qubits with higher fidelity. The Quafu-Qcover allows us to retrieve quantum computer sampling result information at any time using task ID, enabling asynchronous processing. Besides, it includes modules for result preprocessing and visualization, allowing for an intuitive display of the solution to combinatorial optimization problems. We hope that Quafu-Qcover can serve as a guiding example for how to explore application problems on the Quafu cloud quantum computers

5.Typical bipartite steerability and generalized local quantum measurements

Authors:Maximilian Schumacher, Gernot Alber

Abstract: Recently proposed correlation-matrix based sufficient conditions for bipartite steerability from Alice to Bob are applied to local informationally complete positive operator valued measures (POVMs) of the $(N,M)$-type. These POVMs allow for a unified description of a large class of local generalized measurements of current interest. It is shown that this sufficient condition exhibits a peculiar scaling property. It implies that all types of informationally complete $(N,M)$-POVMs are equally powerful in detecting bipartite steerability from Alice to Bob and, in addition, they are as powerful as local orthonormal hermitian operator bases (LOOs). In order to explore the typicality of steering numerical calculations of lower bounds on Euclidean volume ratios between steerable bipartite quantum states from Alice to Bob and all quantum states are determined with the help of a hit-and-run Monte-Carlo algorithm. These results demonstrate that with the single exception of two qubits this correlation-matrix based sufficient condition significantly underestimates these volume ratios. These results are also compared with a recently proposed method which reduces the determination of bipartite steerability from Alice's qubit to Bob's arbitrary dimensional quantum system to the determination of bipartite entanglement. It is demonstrated that in general this method is significantly more effective in detecting typical steerability provided entanglement detection methods are used which transcend local measurements.

6.Uncertainty relations in terms of generalized entropies derived from information diagrams

Authors:Alexey E. Rastegin

Abstract: Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows one to improve relations between various information measures. Measurements of special types are widely used in quantum information science. For many of them we can estimate the index of coincidence defined as the total sum of squared probabilities. Inequalities between entropies and the index of coincidence form a long-standing direction of researches in classical information theory. The so-called information diagrams provide a powerful tool to obtain inequalities of interest. In the literature, results of such a kind mainly deal with standard information functions linked to the Shannon entropy. At the same time, generalized information functions have found use in questions of quantum information theory. In effect, R\'{e}nyi and Tsallis entropies and related functions are of a separate interest. This paper is devoted to entropic uncertainty relations derived from information diagrams. The obtained inequalities are then applied to mutually unbiased bases, symmetric informationally complete measurements and their generalizations. We also improve entropic uncertainty relations for quantum measurement assigned to an equiangular tight frame.

7.Key Rate Analysis of a 3-State Twin-Field Quantum Key Distribution Protocol in the Finite-key Regime

Authors:Matt Young, Darius Bunandar, Marco Lucamarini, Stefano Pirandola

Abstract: When analysing Quantum Key Distribution (QKD) protocols several metrics can be determined, but one of the most important is the Secret Key Rate. The Secret Key Rate is the number of bits per transmission that result in being part of a Secret Key between two parties. There are equations that give the Secret Key Rate, for example, for the BB84 protocol, equation 52 from [1, p.1032] gives the Secret Key Rate for a given Quantum Bit Error Rate (QBER). However, the analysis leading to equations such as these often rely on an Asymptotic approach, where it is assumed that an infinite number of transmissions are sent between the two communicating parties (henceforth denoted as Alice and Bob). In a practical implementation this is obviously impossible. Moreover, some QKD protocols belong to a category called Asymmetric protocols, for which it is significantly more difficult to perform such an analysis. As such, there is currently a lot of investigation into a different approach called the Finite-key regime. Work by Bunandar et al. [2] has produced code that used Semi-Definite Programming to produce lower bounds on the Secret Key Rate of even Asymmetric protocols. Our work looks at devising a novel QKD protocol taking inspiration from both the 3-state version of BB84 [3], and the Twin-Field protocol [4], and then using this code to perform analysis of the new protocol.

8.Nonreciprocal heat flux via synthetic fields in linear quantum systems

Authors:S. -A. Biehs, M. Antezza, G. S. Agarwal

Abstract: We study the heat transfer between N coupled quantum resonators with applied synthetic electric and magnetic fields realized by changing the resonators parameters by external drivings. To this end we develop two general methods, based on the quantum optical master equation and on the Langevin equation for $N$ coupled oscillators where all quantum oscillators can have their own heat baths. The synthetic electric and magnetic fields are generated by a dynamical modulation of the oscillator resonance with a given phase. Using Floquet theory we solve the dynamical equations with both methods which allow us to determine the heat flux spectra and the transferred power. With apply these methods to study the specific case of a linear tight-binding chain of four quantum coupled resonators. We find that in that case, in addition to a non-reciprocal heat flux spectrum already predicted in previous investigations, the synthetic fields induce here non-reciprocity in the total heat flux hence realizing a net heat flux rectification.

9.State preparation in quantum algorithms for fragment-based quantum chemistry

Authors:Ruhee D'Cunha, Matthew Otten, Matthew R. Hermes, Laura Gagliardi, Stephen K. Gray

Abstract: State preparation for quantum algorithms is crucial for achieving high accuracy in quantum chemistry and competing with classical algorithms. The localized active space unitary coupled cluster (LAS-UCC) algorithm iteratively loads a fragment-based multireference wave function onto a quantum computer. In this study, we compare two state preparation methods, quantum phase estimation (QPE) and direct initialization (DI), for each fragment. We analyze the impact of QPE parameters, such as the number of ancilla qubits and Trotter steps, on the prepared state. We find a trade-off between the methods, where DI requires fewer resources for smaller fragments, while QPE is more efficient for larger fragments. Our resource estimates highlight the benefits of system fragmentation in state preparation for subsequent quantum chemical calculations. These findings have broad applications for preparing multireference quantum chemical wave functions on quantum circuits, particularly via QPE circuits.

10.General expansion of natural power of linear combination of Bosonic operators in normal order

Authors:Deepak, Arpita Chatterjee

Abstract: In quantum mechanics, bosonic operators are mathematical objects that are used to represent the creation ($a^\dagger$) and annihilation ($a$) of bosonic particles. The natural power of a linear combination of bosonic operators represents an operator $(a^\dagger x+ay)^n$ with $n$ as the exponent and $x,\,y$ are the variables free from bosonic operators. The normal ordering of these operators is a mathematical technique that arranges the operators so that all the creation operators are to the left of the annihilation operators, reducing the number of terms in the expression. In this paper, we present a general expansion of the natural power of a linear combination of bosonic operators in normal order. We show that the expansion can be expressed in terms of binomial coefficients and the product of the normal-ordered operators using the direct method and than prove it using the fundamental principle of mathematical induction. We also derive a formula for the coefficients of the expansion in terms of the number of bosons and the commutation relation between the creation and annihilation operators. Our results have important applications in the study of many-body systems in quantum mechanics, such as in the calculation of correlation functions and the evaluation of the partition function. The general expansion presented in this paper provides a powerful tool for analyzing and understanding the behavior of bosonic systems, and can be applied to a wide range of physical problems.

11.Universality of graph homomorphism games and the quantum coloring problem

Authors:Samuel J. Harris

Abstract: We show that quantum graph parameters for finite, simple, undirected graphs encode winning strategies for all possible synchronous non-local games. Given a synchronous game $\mathcal{G}=(I,O,\lambda)$ with $|I|=n$ and $|O|=k$, we demonstrate what we call a weak $*$-equivalence between $\mathcal{G}$ and a $3$-coloring game on a graph with at most $3+n+9n(k-2)+6|\lambda^{-1}(\{0\})|$ vertices, strengthening and simplifying work implied by Z. Ji (arXiv:1310.3794) for winning quantum strategies for synchronous non-local games. As an application, we obtain a quantum version of L. Lov\'{a}sz's reduction (Proc. 4th SE Conf. on Comb., Graph Theory & Computing, 1973) of the $k$-coloring problem for a graph $G$ with $n$ vertices and $m$ edges to the $3$-coloring problem for a graph with $3+n+9n(k-2)+6mk$ vertices. We also show that, for ``graph of the game" $X(\mathcal{G})$ associated to $\mathcal{G}$ from A. Atserias et al (J. Comb. Theory Series B, Vol. 136, 2019), the independence number game $\text{Hom}(K_{|I|},\overline{X(\mathcal{G})})$ is hereditarily $*$-equivalent to $\mathcal{G}$, so that the possibility of winning strategies is the same in both games for all models, except the game algebra. Thus, the quantum versions of the chromatic number, independence number and clique number encode winning strategies for all synchronous games in all quantum models.

12.Space-Time-Matter: Some Notes on the Localization Problem in Relativistic Quantum Theory

Authors:Christian Beck

Abstract: This work aims to shed some light on the meaning of the positive energy assumption in relativistic quantum theory and its relation to questions of localization of quantum systems. It is shown that the positive energy property of solutions of relativistic wave equations (such as the Dirac equation) is very fragile with respect to state transformations beyond free time evolution. Paying attention to the connection between negative energy Dirac wave functions and pair creation processes in second quantization, this analysis leads to a better understanding of a class of problems known as the localization problem of relativistic quantum theory (associated for instance with famous results of Newton and Wigner, Reeh and Schlieder, Hegerfeldt or Malament). Finally, this analysis is reflected from the perspective of a Bohmian quantum field theory.

13.Lower-vs-Higher Order Non-classicality of Photon-added Bell-type Entangled Coherent States

Authors:Deepak, Arpita Chatterjee

Abstract: We compare the lower and higher order non-classicality of a class of the photon-added Bell-type entangled coherent states (PBECS) got from Bell-type entangled coherent states using creation operators. We obtained lower and higher order criteria namely Mandel's $Q_m^l$, antibunching $d_h^{l-1}$, Subpoissioning photon statistics $D_h(l-1)$ and Squeezing $S(l)$ for the states obtained. Further we observe that first three criteria does not gives non-classicality for any state and higher order criteria gives very high positive values for all values of parameters. Also the fourth or last criterion $S(l)$ gives non-classicality for lower order as well as higher order.

14.Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging

Authors:Pedro M. Q. Cruz, Bruno Murta

Abstract: The controlled-SWAP and controlled-controlled-NOT gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of classical logic subroutines of quantum algorithms and in quantum schemes with no direct classical counterparts, have made it imperative early on to pursue their efficient decomposition in terms of the lower-level gate sets native to different physical platforms. Here, we add to this body of literature by providing several logically equivalent CNOT-count-optimal circuits for the Toffoli and Fredkin gates under all-to-all and linear qubit connectivity, the latter with two different routings for control and target qubits. We then demonstrate how these decompositions can be employed on near-term quantum computers to mitigate coherent errors via equivalent circuit averaging. We also consider the case where the three qubits on which the Toffoli or Fredkin gates act nontrivially are not adjacent, proposing a novel scheme to reorder them that saves one CNOT for every SWAP. This scheme also finds use in the shallow implementation of long-range CNOTs. Our results highlight the importance of considering different entanglement structures and connectivity constraints when designing efficient quantum circuits.

15.Entanglement dynamics in U(1) symmetric hybrid quantum automaton circuits

Authors:Yiqiu Han, Xiao Chen

Abstract: We study the entanglement dynamics of quantum automaton (QA) circuits in the presence of U(1) symmetry. We find that the second R\'enyi entropy grows diffusively with a logarithmic correction as $\sqrt{t\ln{t}}$, saturating the bound established by Huang [IOP SciNotes 1, 035205 (2020)]. Thanks to the special feature of QA circuits, we understand the entanglement dynamics in terms of a classical bit string model. Specifically, we argue that the diffusive dynamics stems from the rare slow modes containing extensively long domains of spin 0s or 1s. Additionally, we investigate the entanglement dynamics of monitored QA circuits by introducing a composite measurement that preserves both the U(1) symmetry and properties of QA circuits. We find that as the measurement rate increases, there is a transition from a volume-law phase where the second R\'enyi entropy persists the diffusive growth (up to a logarithmic correction) to a critical phase where it grows logarithmically in time. This interesting phenomenon distinguishes QA circuits from non-automaton circuits such as U(1)-symmetric Haar random circuits, where a volume-law to an area-law phase transition exists, and any non-zero rate of projective measurements in the volume-law phase leads to a ballistic growth of the R\'enyi entropy.

16.Extension of exactly-solvable Hamiltonians using symmetries of Lie algebras

Authors:Smik Patel, Tzu-Ching Yen, Artur F. Izmaylov

Abstract: Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki approximations of the evolution operator for the quantum phase estimation algorithm, or in the quantum measurement problem for the variational quantum eigensolver. One of the typical forms of exactly solvable Hamiltonians is a linear combination of operators forming a modest size Lie algebra. Very frequently such linear combinations represent non-interacting Hamiltonians and thus are of limited interest for describing interacting cases. Here we propose the extension where coefficients in these combinations are substituted by polynomials of the Lie algebra symmetries. This substitution results in a more general class of solvable Hamiltonians and for qubit algebras is related to the recently proposed non-contextual Pauli Hamiltonians. In fermionic problems, this substitution leads to Hamiltonians with eigenstates that are single Slater determinants but with different sets of single-particle states for different eigenstates. The new class of solvable Hamiltonians can be measured efficiently using quantum circuits with gates that depend on the result of a mid-circuit measurement of the symmetries.

17.Transfer of quantum states and stationary quantum correlations in a hybrid optomechanical network

Authors:Hugo Molinares, Bing He, Vitalie Eremeev

Abstract: We present a systematic study on the effects of dynamical transfer and steady-state synchronization of quantum states in a hybrid optomechanical network, consisting of two cavities with atoms inside and interacting via a common moving mirror (i.e. mechanical oscillator), are studied. It is found that high fidelity transfer of Schr\"{o}dinger's cat and squeezed states between the cavities modes is possible. Additionally, we show the effect of synchronization of cavity modes in a steady squeezed states at high fidelity realizable by the mechanical oscillator which intermediates the generation, transfer and stabilization of the squeezing. In this framework, we also have studied the generation and evolution of bipartite and tripartite entanglement and found its interconnection to the effects of transfer and synchronization. Particularly, when the transfer occurs at the maximal fidelity, at this instant any entanglement is almost zero, so the modes are disentangled. On the other hand, when the two bosonic modes are synchronized in a squeezed stationary state, then these modes are also entangled. The results found in this study may find their applicability in quantum information and computation technologies, as well in metrology setups, where the squeezed states are essential.

18.Polynomial-time classical sampling of high-temperature quantum Gibbs states

Authors:Chao Yin, Andrew Lucas

Abstract: The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout science, ranging from simulating quantum chemistry to discovering the thermodynamic phase diagram of quantum materials or high-density neutron stars. We present a classical algorithm that samples from a high-temperature quantum Gibbs state in a computational (product state) basis. The runtime grows polynomially with the number of particles, while error vanishes polynomially. This algorithm provides an alternative strategy to existing quantum Monte Carlo methods for overcoming the sign problem. Our result implies that measurement-based quantum computation on a Gibbs state can provide exponential speed up only at sufficiently low temperature, and further constrains what tasks can be exponentially faster on quantum computers.

19.Quantum chi-squared tomography and mutual information testing

Authors:Steven T. Flammia, Ryan O'Donnell

Abstract: For quantum state tomography on rank-$r$ dimension-$d$ states, we show that $\widetilde{O}(r^{.5}d^{1.5}/\epsilon) \leq \widetilde{O}(d^2/\epsilon)$ copies suffice for accuracy $\epsilon$ with respect to (Bures) $\chi^2$-divergence, and $\widetilde{O}(rd/\epsilon)$ copies suffice for accuracy $\epsilon$ with respect to quantum relative entropy. The best previous bound was $\widetilde{O}(rd/\epsilon) \leq \widetilde{O}(d^2/\epsilon)$ with respect to infidelity; our results are an improvement since \[ \text{infidelity} \leq \text{relative entropy} \leq \text{$\chi^2$-divergence}.\] For algorithms that are required to use single-copy measurements, we show that $\widetilde{O}(r^{1.5} d^{1.5}/\epsilon) \leq \widetilde{O}(d^3/\epsilon)$ copies suffice for $\chi^2$-divergence, and $\widetilde{O}(r^{2} d/\epsilon)$ suffice for relative entropy. Using this tomography algorithm, we show that $\widetilde{O}(d^{2.5}/\epsilon)$ copies of a $d\times d$-dimensional bipartite state suffice to test if it has quantum mutual information 0 or at least $\epsilon$. As a corollary, we also improve the best known sample complexity for the classical version of mutual information testing to $\widetilde{O}(d/\epsilon)$.

20.Strictly local Union-Find

Authors:Tim Chan, Simon C. Benjamin

Abstract: Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the growth and merger of data structures through nearest-neighbour steps; this naturally suggests the possibility of realising Union-Find using a lattice of very simple processors with strictly nearest-neighbour links. In this way the computational load can be distributed with near-ideal parallelism. Here we build on earlier work to show for the first time that this strict (rather than partial) locality is practical, with a worst-case runtime $\mathcal O(d^3)$ and mean runtime subquadratic in $d$ where $d$ is the surface code distance. A novel parity-calculation scheme is employed, which can also simplify previously proposed architectures. We compare our strictly local realisation with one augmented by long-range links; while the latter is of course faster, we note that local asynchronous logic could largely negate the difference.

21.Many-body magic via Pauli-Markov chains -- from criticality to gauge theories

Authors:Poetri Sonya Tarabunga, Emanuele Tirrito, Titas Chanda, Marcello Dalmonte

Abstract: We introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains. We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from: in particular, it enables to efficiently extract the magic contained in the correlations between widely-separated subsystems, which characterizes the nonlocality of magic. Our method can be implemented in a variety of situations. We describe an efficient sampling procedure using Tree Tensor Networks, that exploits their hierarchical structure leading to a modest $O(\log N)$ computational scaling with system size. To showcase the applicability and efficiency of our method, we demonstrate the importance of magic in many-body systems via the following discoveries: (a) for one dimensional systems, we show that long-range magic displays strong signatures of conformal quantum criticality (Ising, Potts, and Gaussian), overcoming the limitations of full state magic; (b) in two-dimensional $\mathbb{Z}_2$ lattice gauge theories, we provide conclusive evidence that magic is able to identify the confinement-deconfinement transition, and displays critical scaling behavior even at relatively modest volumes. Finally, we discuss an experimental implementation of the method, which only relies on measurements of Pauli observables.

22.Quantum variational embedding for ground-state energy problems: sum of squares and cluster selection

Authors:Bowen Li, Jianfeng Lu

Abstract: We introduce a sum-of-squares SDP hierarchy approximating the ground-state energy from below for quantum many-body problems, with a natural quantum embedding interpretation. We establish the connections between our approach and other variational methods for lower bounds, including the variational embedding, the RDM method in quantum chemistry, and the Anderson bounds. Additionally, inspired by the quantum information theory, we propose efficient strategies for optimizing cluster selection to tighten SDP relaxations while staying within a computational budget. Numerical experiments are presented to demonstrate the effectiveness of our strategy. As a byproduct of our investigation, we find that quantum entanglement has the potential to capture the underlying graph of the many-body Hamiltonian.

23.Classical and semi-classical limits in phase space

Authors:Clay D. Spence

Abstract: An alternative view of semiclassical mechanics is derived in the form of an approximation to Schr\"odinger's equation, giving a linear first-order partial differential equation on phase space. The equation advectively transports wavefunctions along classical trajectories, so that as a trajectory is followed the amplitude remains constant and the phase changes by the action divided by $\hbar$. The wavefunction's squared-magnitude is a plausible phase space density and obeys Liouville's equation for the classical time evolution of such densities. This is a derivation of the Koopman-von~Neumann (KvN) formulation of classical mechanics, which previously was postulated but not derived. With the time-independent form, quantization arises because continuity constrains the change of phase around any closed path in the torus covered by the classical solution to be an integer multiple of $2\pi$, essentially giving standing waves on the torus. While this applies to any system, for separable systems it gives Bohr-Sommerfeld quantization.

24.Chirped Fractional Stimulated Raman Adiabatic Passage

Authors:Jabir Chathanathil, Aneesh Ramaswamy, Vladimir S. Malinovsky, Dmitry Budker, Svetlana A. Malinovskaya

Abstract: Stimulated Raman Adiabatic Passage (STIRAP) is a widely used method for adiabatic population transfer in a multilevel system. In this work, we study STIRAP under novel conditions and focus on the fractional, F-STIRAP, which is known to create a superposition state with the maximum coherence. In both configurations, STIRAP and F-STIRAP, we implement pulse chirping aiming at a higher contrast, a broader range of parameters for adiabaticity, and enhanced spectral selectivity. Such goals target improvement of quantum imaging, sensing and metrology, and broaden the range of applications of quantum control techniques and protocols. In conventional STIRAP and F-STIRAP, two-photon resonance is required conceptually to satisfy the adiabaticity condition for dynamics within the dark state. Here, we account for a non-zero two-photon detuning and present control schemes to achieve the adiabatic conditions in STIRAP and F-STIRAP through a skillful compensation of the two-photon detuning by pulse chirping. We show that the chirped configuration - C-STIRAP - permits adiabatic passage to a predetermined state among two nearly degenerate final states, when conventional STIRAP fails to resolve them. We demonstrate such a selectivity within a broad range of parameters of the two-photon detuning and the chirp rate. In the C-F-STIRAP, chirping of the pump and the Stokes pulses with different time delays permits a complete compensation of the two-photon detuning and results in a selective maximum coherence of the initial and the target state with higher spectral resolution than in the conventional F-STIRAP.

1.Energetic cost for speedy synchronization in non-Hermitian quantum dynamics

Authors:Maxwell Aifer, Juzar Thingna, Sebastian Deffner

Abstract: Quantum synchronization is crucial for understanding complex dynamics and holds potential applications in quantum computing and communication. Therefore, assessing the thermodynamic resources required for finite-time synchronization in continuous-variable systems is a critical challenge. In the present work, we find these resources to be extensive for large systems. We also bound the speed of quantum and classical synchronization in coupled damped oscillators with non-Hermitian anti-PT-symmetric interactions, and show that the speed of synchronization is limited by the interaction strength relative to the damping. Compared to the classical limit, we find that quantum synchronization is slowed by the non-commutativity of the Hermitian and anti-Hermitian terms. Our general results could be tested experimentally and we suggest an implementation in photonic systems.

2.Measures of contextuality in cyclic systems and the negative probabilities measure CNT3

Authors:Giulio Camillo, Víctor H. Cervantes

Abstract: Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistentlly connected systems). The first of such measures was based on quasi-couplings using negative probabilities (here denoted by CNT3, Dzhafarov & Kujala, 2016). Dzhafarov and Kujala (2019) introduced a measure of contextuality, CNT2, that naturally generalizes to a measure of non-contextuality. Dzhafarov and Kujala (2019) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that that conjecture is correct. Recently, Cervantes (2023) showed the proportionality of CNT2 and the Contextual Fraction measure (CNTF) introduced by Abramsky, Barbosa, and Mansfeld (2017). The present proof completes the description of the interrelations of all contextuality measures as they pertain to cyclic systems.

3.Optical coupling control of isolated mechanical resonators

Authors:F. E. Onah, B. R. Jaramillo-Ávila, F. H. Maldonado-Villamizar, B. M. Rodríguez-Lara

Abstract: We present a Hamiltonian model describing two pairs of mechanical and optical modes under standard optomechanical interaction. The vibrational modes are mechanically isolated from each other and the optical modes couple evanescently. We recover the ranges for variables of interest, such as mechanical and optical resonant frequencies and naked coupling strengths, using a finite element model for a standard experimental realization. We show that the quantum model, under this parameter range and external optical driving, may be approximated into parametric interaction models for all involved modes. As an example, we study the effect of detuning in the optical resonant frequencies modes and optical driving resolved to mechanical sidebands and show an optical beam splitter with interaction strength dressed by the mechanical excitation number, a mechanical bidirectional coupler, and a two-mode mechanical squeezer where the optical state mediates the interaction strength between the mechanical modes.

4.A Gauge Field Theory of Coherent Matter Waves

Authors:Dana Z. Anderson, Katarzyna Krzyzanowska

Abstract: A gauge field treatment of a current, oscillating at a fixed frequency, of interacting neutral atoms leads to a set of matter-wave duals to Maxwell's equations for the electromagnetic field. In contrast to electromagnetics, the velocity of propagation has a lower limit rather than upper limit and the wave impedance of otherwise free space is negative real-valued rather than 377 Ohms. Quantization of the field leads to the matteron, the gauge boson dual to the photon. Unlike the photon, the matteron is bound to an atom and carries negative rather than positive energy, causing the source of the current to undergo cooling. Eigenstates of the combined matter and gauge field annihilation operator define the coherent state of the matter-wave field, which exhibits classical coherence in the limit of large excitation.

5.Detection and Classification of Bipartite and Multipartite Entangled States

Authors:Anu Kumari

Abstract: The detection and classification of entanglement properties in a two-qubit and a multi-qubit system is a topic of great interest. This topic has been extensively studied, and as a result, we discovered various approaches for detecting and classifying multi-qubit, in particular three-qubit entangled states. The emphasis of this work is on a formalism of methods for the detection and classification of bipartite as well as multipartite quantum systems. We have used the method of structural physical approximation of partially transposed matrix (SPA-PT) for the detection of entangled states in arbitrary dimensional bipartite quantum systems. Also, we have proposed criteria for the classification of all possible stochastic local operations and classical communication (SLOCC) inequivalent classes of a pure and mixed three-qubit state using the SPA-PT map. To quantify entanglement, we have defined a new measure of entanglement based on the method of SPA-PT, which we named as "structured negativity". We have shown that this measure can be used to quantify entanglement for negative partial transposed entangled states (NPTES). Since the methods for detection, classification and quantification of entanglement, defined in this thesis are based on SPA-PT, they may be realized in an experiment.

6.Quantum Speedup for the Maximum Cut Problem

Authors:Weng-Long Chang, Renata Wong, Wen-Yu Chung, Yu-Hao Chen, Ju-Chin Chen, Athanasios V. Vasilakos

Abstract: Given an undirected, unweighted graph with $n$ vertices and $m$ edges, the maximum cut problem is to find a partition of the $n$ vertices into disjoint subsets $V_1$ and $V_2$ such that the number of edges between them is as large as possible. Classically, it is an NP-complete problem, which has potential applications ranging from circuit layout design, statistical physics, computer vision, machine learning and network science to clustering. In this paper, we propose a quantum algorithm to solve the maximum cut problem for any graph $G$ with a quadratic speedup over its classical counterparts, where the temporal and spatial complexities are reduced to, respectively, $O(\sqrt{2^n/r})$ and $O(m^2)$. With respect to oracle-related quantum algorithms for NP-complete problems, we identify our algorithm as optimal. Furthermore, to justify the feasibility of the proposed algorithm, we successfully solve a typical maximum cut problem for a graph with three vertices and two edges by carrying out experiments on IBM's quantum computer.

7.Quantum logical controlled-NOT gate in a lithium niobate-on-insulator photonic quantum walk

Authors:Robert J. Chapman, Samuel Häusler, Giovanni Finco, Fabian Kaufmann, Rachel Grange

Abstract: Quantum computers comprise elementary logic gates that initialize, control and measure delicate quantum states. One of the most important gates is the controlled-NOT, which is widely used to prepare two-qubit entangled states. The controlled-NOT gate for single photon qubits is normally realized as a six-mode network of individual beamsplitters. This architecture however, utilizes only a small fraction of the circuit for the quantum operation with the majority of the footprint dedicated to routing waveguides. Quantum walks are an alternative photonics platform that use arrays of coupled waveguides with a continuous interaction region instead of discrete gates. While quantum walks have been successful for investigating condensed matter physics, applying the multi-mode interference for logical quantum operations is yet to be shown. Here, we experimentally demonstrate a two-qubit controlled-NOT gate in an array of lithium niobate-on-insulator waveguides. We engineer the tight-binding Hamiltonian of the six evanescently-coupled single-mode waveguides such that the multi-mode interference corresponds to the linear optical controlled-NOT unitary. We measure the two-qubit transfer matrix with $0.938\pm0.003$ fidelity, and we use the gate to generate entangled qubits with $0.945\pm0.002$ fidelity by preparing the control photon in a superposition state. Our results highlight a new application for quantum walks that use a compact multi-mode interaction region to realize large multi-component quantum circuits.

8.Thermally driven quantum refrigerator autonomously resets superconducting qubit

Authors:Mohammed Ali Aamir, Paul Jamet Suria, José Antonio Marín Guzmán, Claudia Castillo-Moreno, Jeffrey M. Epstein, Nicole Yunger Halpern, Simone Gasparinetti

Abstract: The first thermal machines steered the industrial revolution, but their quantum analogs have yet to prove useful. Here, we demonstrate a useful quantum absorption refrigerator formed from superconducting circuits. We use it to reset a transmon qubit to a temperature lower than that achievable with any one available bath. The process is driven by a thermal gradient and is autonomous -- requires no external control. The refrigerator exploits an engineered three-body interaction between the target qubit and two auxiliary qudits coupled to thermal environments. The environments consist of microwave waveguides populated with synthesized thermal photons. The target qubit, if initially fully excited, reaches a steady-state excited-level population of $5\times10^{-4} \pm 5\times10^{-4}$ (an effective temperature of 23.5~mK) in about 1.6~$\mu$s. Our results epitomize how quantum thermal machines can be leveraged for quantum information-processing tasks. They also initiate a path toward experimental studies of quantum thermodynamics with superconducting circuits coupled to propagating thermal microwave fields.

9.Quantum field theoretical framework for the electromagnetic response of graphene and dispersion relations with implications to the Casimir effect

Authors:G. L. Klimchitskaya, V. M. Mostepanenko

Abstract: The spatially nonlocal response functions of graphene obtained on the basis of first principles of quantum field theory using the polarization tensor are considered in the areas of both the on-the-mass-shell and off-the-mass-shell waves. It s shown that at zero frequency the longitudinal permittivity of graphene is the regular function, whereas the transverse one possesses a double pole for any nonzero wave vector. According to our results, both the longitudinal and transverse permittivities satisfy the dispersion (Kramers-Kronig) relations connecting their real and imaginary parts, as well as expressing each of these permittivities along the imaginary frequency axis via its imaginary part. For the transverse permittivity, the form of an additional term arising in the dispersion relations due to the presence of a double pole is found. The form of dispersion relations is unaffected by the branch points which arise on the real frequency axis in the presence of spatial nonlocality. The obtained results are discussed in connection with the well known problem of the Lifshitz theory which was found to be in conflict with the measurement data when using the much studied response function of metals. A possible way of attack on this problem based on the case of graphene is suggested.

10.Quantum work extraction efficiency for noisy quantum batteries: the role of coherence

Authors:Salvatore Tirone, Raffaele Salvia, Stefano Chessa, Vittorio Giovannetti

Abstract: Quantum work capacitances and maximal asymptotic work/energy ratios are figures of merit characterizing the robustness against noise of work extraction processes in quantum batteries formed by collections of quantum systems. In this paper we establish a direct connection between these functionals and, exploiting this result, we analyze different types of noise models mimicking self-discharging, thermalization and dephasing effects. In this context we show that input quantum coherence can significantly improve the storage performance of noisy quantum batteries and that the maximum output ergotropy is not always achieved by the maximum available input energy.

11.An intrinsic causality principle in histories-based quantum theory: a proposal

Authors:Fay Dowker, Rafael D. Sorkin

Abstract: Relativistic causality (RC) is the principle that no cause can act outside its future lightcone, but any attempt to formulate this principle more precisely will depend on the foundational framework that one adopts for quantum theory. Adopting a histories-based (or "path integral") framework, we relate RC to a condition we term "Persistence of Zero" (PoZ), according to which an event $E$ of measure zero remains forbidden if one forms its conjunction with any other event associated to a spacetime region that is later than or spacelike to that of $E$. We also relate PoZ to the Bell inequalities by showing that, in combination with a second, more technical condition it leads to the quantal counterpart of Fine's patching theorem in much the same way as Bell's condition of Local Causality leads to Fine's original theorem. We then argue that RC per se has very little to say on the matter of which correlations can occur in nature and which cannot. From the point of view we arrive at, histories-based quantum theories are nonlocal in spacetime, and fully in compliance with relativistic causality.

12.Logarithmic Negativity and Spectrum in Free Fermionic Systems for Well-separated Intervals

Authors:Eldad Bettelheim

Abstract: We employ a mathematical framework based on the Riemann-Hilbert approach developed in Ref. [1] to study logarithmic negativity of two intervals of free fermions in the case where the size of the intervals as well as the distance between them is macroscopic. We find that none of the eigenvalues of the density matrix become negative, but rather they develop a small imaginary value, leading to non-zero logarithmic negativity. As an example, we compute negativity at half-filling and for intervals of equal size we find a result of order $(\log(N))^{-1}$, where $N$ is the typical length scale in units of the lattice spacing. One may compute logarithmic negativity in further situations, but we find that the results are non-universal, depending non-smoothly on the Fermi level and the size of the intervals in units of the lattice spacing.

13.Sequential measurements and the Kochen-Specker arguments

Authors:Gábor Hofer-Szabó

Abstract: It will be shown that the Peres-Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential measurements allow for noncontextual models in which hidden states update between consecutive measurements. Two recent experiments realizing the Peres-Mermin square by sequential measurements will also be analyzed along with other hidden-variable models accounting for these experiments.

14.Measurement incompatibility is strictly stronger than disturbance

Authors:Marco Erba, Paolo Perinotti, Davide Rolino, Alessandro Tosini

Abstract: The core of Heisenberg's argument for the uncertainty principle, involving the famous $\gamma$-ray microscope $\textit{Gedankenexperiment}$, consists in the existence of measurements that irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. The argument was put forward to justify the existence of incompatible measurements, namely, measurements that cannot be performed jointly. In this Letter, on the one hand, we provide a compelling argument showing that incompatibility is indeed a sufficient condition for disturbance, while, on the other hand, we exhibit a toy theory that is a counterexample for the converse implication.

15.Potential scatterings in $L^2$ space: (1) non-orthogonality of stationary states

Authors:Kenzo Ishikawa

Abstract: Orthogonality of eigenstates of different energies held in bound states plays important roles, but is dubious in scattering states. Scalar products of stationary scattering states are analyzed using solvable models, and an orthogonality is shown violated in majority potentials. Consequently their superposition has time dependent norm and is not suitable for a physical state. Various exceptional cases are clarified. From the results of the first paper,a perturbative and variational methods emerge as viable methods for finding a transition probability of normalized initial and final states.

16.Potential scattering in $L^2$ space: (2) Rigorous scattering probability of wave packets

Authors:Kenzo Ishikawa

Abstract: Potential scatterings in experimental setups are formulated using a complete set of normalized states for initial and final states. Various ambiguities in a standard method caused by non-orthogonality of stationary states are resolved, and consistent scattering probabilities that clarify an interference at a forward scattering are found. A power series expansions in the coupling strength satisfying manifest unitarity is presented, and a variational method for the transition probability is proposed.

17.Probing scrambling and operator size distributions using random mixed states and local measurements

Authors:Philip Daniel Blocher, Karthik Chinni, Sivaprasad Omanakuttan, Pablo M. Poggi

Abstract: The dynamical spreading of quantum information through a many-body system, typically called scrambling, is a complex process that has proven to be essential to describe many properties of out-of-equilibrium quantum systems. Scrambling can, in principle, be fully characterized via the use of out-of-time-ordered correlation functions, which are notoriously hard to access experimentally. In this work, we put forward an alternative toolbox of measurement protocols to experimentally probe scrambling by accessing properties of the operator size probability distribution, which tracks the size of the support of observables in a many-body system over time. Our measurement protocols require the preparation of separable mixed states together with local operations and measurements, and combine the tools of randomized operations, a modern development of near-term quantum algorithms, with the use of mixed states, a standard tool in NMR experiments. We demonstrate how to efficiently probe the probability-generating function of the operator distribution and discuss the challenges associated with obtaining the moments of the operator distribution. We further show that manipulating the initial state of the protocol allows us to directly obtain the individual elements of the distribution for small system sizes.

18.Robotic vectorial field alignment for spin-based quantum sensors

Authors:Joe A. Smith, Dandan Zhang, Krishna C. Balram

Abstract: Developing practical quantum technologies will require the exquisite manipulation of fragile systems in a robust and repeatable way. As quantum technologies move towards real world applications, from biological sensing to communication in space, increasing experimental complexity introduces constraints that can be alleviated by the introduction of new technologies. Robotics has shown tremendous technological progress by realising increasingly smart, autonomous and highly dexterous machines. Here, we show that a robot can sensitise an NV centre quantum magnetometer. We demonstrate that a robotic arm equipped with a magnet can traverse a highly complex experimental setting to provide a vector magnetic field with up to $1^\circ$ angular accuracy and below 0.1 mT amplitude error, and determine the orientation of a single stochastically-aligned spin-based sensor. Our work opens up the prospect of integrating robotics across many quantum degrees of freedom in constrained environments, allowing for increased prototyping speed, control, and robustness in quantum technology applications.

19.Quantum simulations of time-dependent Hamiltonians beyond the quasi-static approximation

Authors:Boyuan Shi, Florian Mintert

Abstract: Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to the time-independence of the systems to be simulated. We overcome this restriction to perturbative approaches and demonstrate the potential of achievable quantum simulations with the pedagogical example of a Lambda-system and the quench in finite time through a quantum phase transition of a Chern insulator in a driven Hubbard system.

20.Simulation of quantum optics by coherent state decomposition

Authors:Jeffrey Marshall, Namit Anand

Abstract: We introduce a framework for simulating quantum optics by decomposing the system into a finite rank (number of terms) superposition of coherent states. This allows us to define a resource theory, where linear optical operations are `free' (i.e., do not increase the rank), and the simulation complexity for an $m$-mode system scales quadratically in $m$, in stark contrast to the Hilbert space dimension. We outline this approach explicitly in the Fock basis, relevant in particular for Boson sampling, where the simulation time (space) complexity for computing output amplitudes, to arbitrary accuracy, scales as $O(m^2 2^n)$ ($O(m2^n)$), for $n$ photons distributed amongst $m$ modes. We additionally demonstrate linear optical simulations with the $n$ photons initially in the same mode scales efficiently, as $O(m^2 n)$. This paradigm provides a practical notion of `non-classicality', i.e., the classical resources required for simulation, which by making connections to the stellar formalism, we show this comes from two independent contributions, the number of single-photon additions, and the amount of squeezing.

21.Quantum-embeddable stochastic matrices

Authors:Fereshte Shahbeigi, Christopher T. Chubb, Ryszard Kukulski, Łukasz Pawela, Kamil Korzekwa

Abstract: The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the quantum version of this problem, asking of the existence of a Markovian quantum channel generating state transitions described by a given $T$. More precisely, we aim at characterising the set of quantum-embeddable stochastic matrices that arise from memoryless continuous-time quantum evolution. To this end, we derive both upper and lower bounds on that set, providing new families of stochastic matrices that are quantum-embeddable but not classically-embeddable, as well as families of stochastic matrices that are not quantum-embeddable. As a result, we demonstrate that a larger set of transition matrices can be explained by memoryless models if the dynamics is allowed to be quantum, but we also identify a non-zero measure set of random processes that cannot be explained by either classical or quantum memoryless dynamics. Finally, we fully characterise extreme stochastic matrices (with entries given only by zeros and ones) that are quantum-embeddable.

22.A solvable model for graph state decoherence dynamics

Authors:Jérôme Houdayer, Haggai Landa, Grégoire Misguich

Abstract: We present an exactly solvable toy model for the continuous dissipative dynamics of permutation-invariant graph states of N qubits. Such states are locally equivalent to an N-qubit Greenberger-Horne-Zeilinger (GHZ) state, a fundamental resource in many quantum information processing setups. We focus on the time evolution of the state governed by a Lindblad master equation with the three standard single-qubit jump operators, the Hamiltonian part being set to zero. Deriving analytic expressions for the expectation values of observables expanded in the Pauli basis at all times, we analyze the nontrivial intermediate-time dynamics. Using a numerical solver based on matrix product operators we simulate the time evolution for systems with up to 64 qubits and verify a numerically exact agreement with the analytical results. We find that the evolution of the operator space entanglement entropy of a bipartition of the system manifests a plateau whose duration increases logarithmically with the number of qubits, whereas all Pauli-operator products have expectation values decaying at most in constant time.

23.Validating phase-space methods with tensor networks in two-dimensional spin models with power-law interactions

Authors:Sean R. Muleady, Mingru Yang, Steven R. White, Ana Maria Rey

Abstract: Using a recently developed extension of the time-dependent variational principle for matrix product states, we evaluate the dynamics of 2D power-law interacting XXZ models, implementable in a variety of state-of-the-art experimental platforms. We compute the spin squeezing as a measure of correlations in the system, and compare to semiclassical phase-space calculations utilizing the discrete truncated Wigner approximation (DTWA). We find the latter efficiently and accurately captures the scaling of entanglement with system size in these systems, despite the comparatively resource-intensive tensor network representation of the dynamics. We also compare the steady-state behavior of DTWA to thermal ensemble calculations with tensor networks. Our results open a way to benchmark dynamical calculations for two-dimensional quantum systems, and allow us to rigorously validate recent predictions for the generation of scalable entangled resources for metrology in these systems.

24.Simulating quantum computation with magic states: how many "bits" for "it"?

Authors:Michael Zurel, Cihan Okay, Robert Raussendorf

Abstract: A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling algorithms based on Wigner functions, with the important distinction that Wigner functions can take negative values obstructing the sampling. Indeed, negativity in Wigner functions has been identified as a precondition for a quantum speed-up. However, in the present method of classical simulation, negativity of quasiprobability functions never arises. This model remains probabilistic for all quantum computations. In this paper, we analyze the amount of classical data that the simulation procedure must track. We find that this amount is small. Specifically, for any number $n$ of magic states, the number of bits that describe the quantum system at any given time is $2n^2+O(n)$.

1.Coherence Filtration under Strictly Incoherent Operations

Authors:C. L. Liu, C. P. Sun

Abstract: We study the task of coherence filtration under strictly incoherent operations in this paper. The aim of this task is to transform a given state $\rho$ into another one $\rho^\prime$ whose fidelity with the maximally coherent state is maximal by using stochastic strictly incoherent operations. We find that the maximal fidelity between $\rho^\prime$ and the maximally coherent state is given by a multiple of the $\Delta$ robustness of coherence $R(\rho\|\Delta\rho):=\min\{\uplambda|\rho\leq\uplambda\Delta\rho\}$, which provides $R(\rho\|\Delta\rho)$ an operational interpretation. Finally, we provide a coherence measure based on the task of coherence filtration.

2.A Scalable, Fast and Programmable Neural Decoder for Fault-Tolerant Quantum Computation Using Surface Codes

Authors:Mengyu Zhang, Xiangyu Ren, Guanglei Xi, Zhenxing Zhang, Qiaonian Yu, Fuming Liu, Hualiang Zhang, Shengyu Zhang, Yi-Cong Zheng

Abstract: Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms. However, realizing practical quantum error correction (QEC) requires resolving many challenges to implement a high-performance real-time decoding system. Many decoding algorithms have been proposed and optimized in the past few decades, of which neural network (NNs) based solutions have drawn an increasing amount of attention due to their high efficiency. Unfortunately, previous works on neural decoders are still at an early stage and have only relatively simple architectures, which makes them unsuitable for practical QEC. In this work, we propose a scalable, fast, and programmable neural decoding system to meet the requirements of FTQEC for rotated surface codes (RSC). Firstly, we propose a hardware-efficient NN decoding algorithm with relatively low complexity and high accuracy. Secondly, we develop a customized hardware decoder with architectural optimizations to reduce latency. Thirdly, our proposed programmable architecture boosts the scalability and flexibility of the decoder by maximizing parallelism. Fourthly, we build an FPGA-based decoding system with integrated control hardware for evaluation. Our $L=5$ ($L$ is the code distance) decoder achieves an extremely low decoding latency of 197 ns, and the $L=7$ configuration also requires only 1.136 $\mu$s, both taking $2L$ rounds of syndrome measurements. The accuracy results of our system are close to minimum weight perfect matching (MWPM). Furthermore, our programmable architecture reduces hardware resource consumption by up to $3.0\times$ with only a small latency loss. We validated our approach in real-world scenarios by conducting a proof-of-concept benchmark with practical noise models, including one derived from experimental data gathered from physical hardware.

3.Signatures of dynamically dressed states

Authors:Katarina Boos, Sang Kyu Kim, Thomas Bracht, Friedrich Sbresny, Jan Kaspari, Moritz Cygorek, Hubert Riedl, Frederik W. Bopp, William Rauhaus, Carolin Calcagno, Jonathan J. Finley, Doris E. Reiter, Kai Mueller

Abstract: The interaction of a resonant light field with a quantum two-level system is of key interest both for fundamental quantum optics and quantum technological applications employing resonant excitation. While emission under resonant continuous-wave excitation has been well-studied, the more complex emission spectrum of dynamically dressed states, a quantum two-level system driven by resonant pulsed excitation, has so far been investigated in detail only theoretically. Here, we present the first experimental observation of the complete resonance fluorescence emission spectrum of a single quantum two-level system, in form of an excitonic transition in a semiconductor quantum dot, driven by finite Gaussian pulses. We observe multiple emerging sidebands as predicted by theory with an increase of their number and spectral detuning with excitation pulse intensity and a dependence of their spectral shape and intensity on the pulse length. Detuning-dependent measurements provide additional insights into the emission features. The experimental results are in excellent agreement with theoretical calculations of the emission spectra, corroborating our findings.

4.Asymmetry-enhanced phase sensing via asymmetric entangled coherent states

Authors:Xiao-Tong Chen, Wang-Jun Lu, Yunlan Zuo, Rui Zhang, Ya-Feng Jiao, Le-Man Kuang

Abstract: We study quantum phase sensing with an asymmetric two-mode entangled coherent state (ECS) in which the two local amplitudes have different values. We find the phenomenon of the asymmetry-enhanced phase sensing which the asymmetry can significantly increase the precise of the phase estimation. We further study the effect of decoherence induced by the photon loss on quantum phase sensing. It is shown that the asymmetric ECSs have stronger capability against decoherence over the symmetric ECSs. It is indicated that the asymmetric ECSs have obvious advantages over the symmetric ECSs in the quantum phase sensing. We also study the practical phase sensing scheme with the intensity-difference measurement, and show that the asymmetry in the asymmetric ECSs can enhance the phase sensitivity in the practical phase measurement scheme. Our work reveals the asymmetry in the asymmetric ECSs is a new quantum-sensing resource, and opens a new way to the ultra-sensitive quantum phase sensing in the presence of photon losses.

5.Effects of experimental impairments on the security of continuous-variable quantum key distribution

Authors:Andres Ruiz-Chamorro, Daniel Cano, Aida Garcia-Callejo, Veronica Fernandez

Abstract: Quantum Key Distribution (QKD) is a cutting-edge communication method that enables secure communication between two parties. Continuous-variable QKD (CV-QKD) is a promising approach to QKD that has several advantages over traditional discrete-variable systems. Despite its potential, CV-QKD systems are highly sensitive to optical and electronic component impairments, which can significantly reduce the secret key rate. In this research, we address this challenge by modeling a CV-QKD system to simulate the impact of individual impairments on the secret key rate. The results show that laser frequency drifts and small imperfections in electro-optical devices such as the beam splitter and the balanced detector have a negative impact on the secret key rate. This provides valuable insights into strategies for optimizing the performance of CV-QKD systems and overcome limitations caused by component impairments. By offering a method to analyze them, the study enables the establishment of quality standards for the components of CV-QKD systems, driving the development of advanced technologies for secure communication in the future.

6.Near-Perfect Logical Magic State Preparation on a Superconducting Quantum Processor

Authors:Yangsen Ye, Tan He, He-Liang Huang, Zuolin Wei, Yiming Zhang, Youwei Zhao, Dachao Wu, Qingling Zhu, Huijie Guan, Sirui Cao, Fusheng Chen, Tung-Hsun Chung, Hui Deng, Daojin Fan, Ming Gong, Cheng Guo, Shaojun Guo, Lianchen Han, Na Li, Shaowei Li, Yuan Li, Futian Liang, Jin Lin, Haoran Qian, Hao Rong, Hong Su, Shiyu Wang, Yulin Wu, Yu Xu, Chong Ying, Jiale Yu, Chen Zha, Kaili Zhang, Yong-Heng Huo, Chao-Yang Lu, Cheng-Zhi Peng, Xiaobo Zhu, Jian-Wei Pan

Abstract: Fault-tolerant quantum computing based on surface code has emerged as an attractive candidate for practical large-scale quantum computers to achieve robust noise resistance. To achieve universality, magic states preparation is a commonly approach for introducing non-Clifford gates. Here, we present a hardware-efficient and scalable protocol for arbitrary logical state preparation for the rotated surface code, and further experimentally implement it on the \textit{Zuchongzhi} 2.1 superconducting quantum processor. An average of $0.9943 \pm 0.0002$ logical fidelity at different logical states with distance-three is achieved. In particular, the magic state ${|A^{\pi/4}\rangle}_L$ is prepared with logical fidelity of $0.9997 \pm 0.0009 $, which is significantly higher than the state distillation protocol threshold, 0.859, and even higher than the average fidelity of all physical gate operations. Our work provides a viable and efficient avenue for generating high-fidelity raw logical magic states, which is essential for realizing non-Clifford logical gates in the surface code.

7.Demonstration of the excited-state search on the D-wave quantum annealer

Authors:Takashi Imoto, Yuki Susa, Ryoji Miyazaki, Tadashi Kadowaki, Yuichiro Matsuzaki

Abstract: Quantum annealing is a way to prepare an eigenstate of the problem Hamiltonian. Starting from an eigenstate of a trivial Hamiltonian, we slowly change the Hamiltonian to the problem Hamiltonian, and the system remains in the eigenstate of the Hamiltonian as long as the so-called adiabatic condition is satisfied. By using devices provided by D-Wave Systems Inc., there were experimental demonstrations to prepare a ground state of the problem Hamiltonian. However, up to date, there are no demonstrations to prepare the excited state of the problem Hamiltonian with quantum annealing. Here, we demonstrate the excited-state search by using the D-wave processor. The key idea is to use the reverse quantum annealing with a hot start where the initial state is the excited state of the trivial Hamiltonian. During the reverse quantum annealing, we control not only the transverse field but also the longitudinal field and slowly change the Hamiltonian to the problem Hamiltonian so that we can obtain the desired excited state. As an example of the exited state search, we adopt a two-qubit Ising model as the problem Hamiltonian and succeed to prepare the excited state. Also, we solve the shortest vector problem where the solution is embedded into the first excited state of the Ising Hamiltonian. Our results pave the way for new applications of quantum annealers to use the excited states.

8.Quantum-Discrete-Map-Based Recurrent Neural Networks

Authors:Tai-Ping Sun, Zhao-Yun Chen, Cheng Xue, Shi-Xin Ma, Huan-Yu Liu, Yu-Chun Wu, Guo-Ping Guo

Abstract: Quantum machine learning is a rapidly growing domain and its potential has been explored for time series prediction and dynamics simulation in existing works. In this study, we propose a quantum-discrete-map-based recurrent neural network (QDM-RNN) to overcome the limitations posed by the circuit depth growing with the length of time series. From a discrete-dynamical perspective, quantum circuits are leveraged to build the discrete map and hence the discrete dynamical system. This approach involves measuring partial qubits to obtain historical information (memory) that is reused in the encoding layer of next time step, and measuring the other qubits to retrieve classical information as output. The nonlinear properties of the quantum discrete map make it appealing for embedding low-dimensional dynamics into higher dimensions, which is consistent with recurrent learning tricks. In numerical simulations, the QDM-RNN is implemented with one-feature datasets of waves and two-feature datasets of dynamics to demonstrate its capability. Our study introduces a new paradigm for quantum machine learning and highlights the potential of quantum computing in nonlinear dynamics.

9.Efficient and secure quantum network coding based on quantum full homomorphic encryption

Authors:Ning Wang, Fei Gao, Song Lin

Abstract: Based on $d$-dimensional quantum full homomorphic encryption, an efficient and secure quantum network coding protocol is proposed in this paper. First, a quantum full homomorphic encryption protocol is constructed utilizing $d$-dimensional universal quantum gates. On this basis, an efficient quantum network coding protocol is proposed. In the protocol, two source nodes encrypt their respective prepared quantum states with the quantum full homomorphic encryption protocol. The two intermediate nodes successively perform homomorphic evaluation of the received quantum states. Finally, the two sink nodes recover the quantum states transmitted by the two source nodes in the butterfly network depending on their measurement results. The performance analysis shows that the proposed quantum network coding protocol is correct and resistant to attacks launched by dishonest intermediate nodes and external eavesdroppers. Compared to related protocols, the proposed protocol not only enables to transfer information in $d$-dimensional quantum system, but also requires only 1 quantum gate and a key of length 2 in the encryption phase, which makes the protocol has higher efficiency.

10.GHz configurable photon pair generation from a silicon nonlinear interferometer

Authors:Jonathan Frazer, Takafumi Ono, Jonathan C. F. Matthews

Abstract: Low loss and high speed processing of photons is central to architectures for photonic quantum information. High speed switching enables non-deterministic photon sources and logic gates to be made deterministic, while the speed with which quantum light sources can be turned on and off impacts the clock rate of photonic computers and the data rate of quantum communication. Here we use lossy carrier depletion modulators in a silicon waveguide nonlinear interferometer to modulate photon pair generation at 1~GHz without exposing the generated photons to the phase dependent parasitic loss of the modulators. The super sensitivity of nonlinear interferometers reduces power consumption compared to modulating the driving laser. This can be a building block component for high speed programmabile, generalised nonlinear waveguide networks.

11.Plug-and-play measurement of chromatic dispersion by means of two-photon interferometry

Authors:Romain Dalidet, Anthony Martin, Mattis Riesner, Sidi-Ely Ahmedou, Romain Dauliat, Baptiste Leconte, Guillaume Walter, Grégory Sauder, Jean-Christophe Delagnes, Guy Millot, Philippe Roy, Raphaël Jamier, Sébastien Tanzilli, Laurent Labonté

Abstract: Since the first proof-of-principle experiments 25 years ago, quantum metrology has matured from fundamental concepts to versatile and powerful tools in a large variety of research branches, such as gravitational-wave detection, atomic clocks, plasmonic sensing, and magnetometry. At the same time, two-photon interferometry, which underpins the possibility of entanglement to probe optical materials with unprecedented levels of precision and accuracy, holds the promise to stand at the heart of innovative functional quantum sensing systems. We report a novel quantum-based method for measuring the frequency dependence of the velocity in a transparent medium, i.e, the chromatic dispersion (CD). This technique, using energy-time entangled photons, allows straightforward access to CD value from the visibility of two-photon fringes recorded in a free evolution regime. In addition, our quantum approach features all advantages of classical measurement techniques, i.e, flexibility and accuracy, all in a plug-and-play system.

12.Alternating quantum-emitter chains: Exceptional-point phase transition, edge state, and quantum walks

Authors:Jimin Li, Zongping Gong

Abstract: We study the long-range hopping limit of a one-dimensional array of $N$ equal-distanced quantum emitters in free space, where the hopping amplitude of emitter excitation is proportional to the inverse of the distance and equals the lattice dimension. For two species of emitters in an alternating arrangement, the single excitation sector exhibits non-Hermitian spectral singularities known as exceptional points. We unveil an unconventional phase transition, dubbed exceptional-point phase transition, from the collective to individual spontaneous emission behaviors. At the transition point, the $N \times N$ Hamiltonian fragments into $N/2-1$ many two-dimensional non-diagonalizable blocks. The remaining diagonalizable block contains a dissipation-induced edge state with algebraically localized profiles, and we provide numerical evidence for its existence in the infinite-array limit. We demonstrate that the edge state can be eliminated via a continuous deformation, consistent with the ill-definedness of bulk topological invariant. We also propose a spatially resolved character to quantify the incoherent flow and loss in the non-unitary quantum walks of single atomic excitations.

13.Quantum Random Number Generator Based on LED

Authors:Mohammadreza Moeini, Mohsen Akbari, Mohammad Mirsadeghi, Hamid Reza Naeij, Nima Haghkish, Ali Hayeri, Mehrdad Malekian

Abstract: Quantum Random Number Generators Produce random numbers based on the intrinsic probability nature of quantum mechanics, making them true random number generators. In this paper, we design and fabricate an embedded QRNG that produces random numbers based on fluctuations of spontaneous emission in a LED. Additionally, a new perspective on the randomness of the recombination process in a LED is introduced that is consistent with experimental results. To achieve a robust and reliable QRNGm we compare some usual post processing methods and select the best one for a real time device. This device could pass NIST tests, the output speed is 1 Mbit per S and the randomness of the output data is invariant in time and different temperatures.

14.Hidden variables, free choice, context-independence, and all that

Authors:Ehtibar N. Dzhafarov

Abstract: This paper provides a systematic account of the hidden variable models (HVMs) formulated to describe systems of random variables with mutually exclusive contexts. Any such system can be equivalently described either by a model with free choice but generally context-dependent mapping of the hidden variables into observable ones, or by a model with context-independent mapping but generally compromised free choice. These two HVMs are unfalsifiable, applicable to all possible systems. This implies that freedom of choice and context-independent mapping are no assumptions at all, and they tell us nothing about freedom of choice or physical influences exerted by contexts as these notions would be understood in science and philosophy. The conjunction of these two notions, however, defines a falsifiable HVM that describes noncontextuality when applied to systems with no disturbance or to consistifications of arbitrary systems. This HVM is most adequately captured by the term ``context-irrelevance,'' meaning that no distribution in the model changes with context.

15.Quantifying environment non-classicality in dissipative open quantum dynamics

Authors:Adrián A. Budini

Abstract: Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. By restricting to dissipative dynamics, here we propose a measure that quantifies how far the environment action on a system departs from the influence of classical noise fluctuations. It relies on the lack of commutativity between the initial reservoir state and the system-environment total Hamiltonian. Independently of the nature of the dissipative system evolution, Markovian or non-Markovian, the measure can be written in terms of the dual propagator that defines the evolution of system operators. The physical meaning and properties of the proposed definition are discussed in detail and also characterized through different paradigmatic dissipative Markovian and non-Markovian open quantum dynamics.

16.Time delay statistics for chaotic cavities with absorption

Authors:Marcel Novaes

Abstract: We present a semiclassical approach for time delay statistics in quantum chaotic systems, in the presence of absorption, for broken time-reversal symmetry. We derive three kinds of expressions for Schur-moments of the time delay operator: as a power series in inverse channel number, $1/M$, whose coefficients are rational functions of absorption time, $\tau_a$; as a power series in $\tau_a$, tailored to strong absorption, whose coefficients are rational functions of $M$; as a power series in $1/\tau_a$, tailored to weak absorption, whose coefficients are rational functions of $M$.

17.Non-Hermitian Floquet Topological Matter -- A Review

Authors:Longwen Zhou, Da-Jian Zhang

Abstract: Non-Hermitian Floquet topological phases appear in systems described by time-periodic non-Hermitian Hamiltonians. This review presents a sum-up of our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. After a brief overview of the literature, we introduce our theoretical framework for the study of non-Hermitian Floquet systems and the topological characterization of non-Hermitian Floquet bands. Based on our theories, we describe typical examples of non-Hermitian Floquet topological insulators, superconductors and quasicrystals with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties and localization transitions. We conclude this review by summarizing our main discoveries and discussing potential future directions.

18.Effective Rationality for Local Unitary Invariants of Mixed States of Two Qubits

Authors:Luca Candelori, Vladimir Y. Chernyak, John R. Klein, Nick Rekuski

Abstract: We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian group. From this construction, we are able to give explicit expressions for the generating invariants in terms of the Bloch matrix representation of mixed states of two qubits. We also prove similar rationality statements for the local unitary invariants of symmetric mixed states of two qubits. Our results apply to both complex-valued and real-valued invariants.

19.The Evolution of the Bell Notion of Beable: from Bohr to Primitive Ontology

Authors:Federico Laudisa

Abstract: John S. Bell introduced the notion of beable, as opposed to the standard notion of observable, in order to emphasize the need for an unambiguous formulation of quantum mechanics. In the paper I show that Bell formulated in fact two different theories of beables. The first is somehow reminiscent of the Bohr views on quantum mechanics but, at the same time, is curiously adopted by Bell as a critical tool against the Copenhagen interpretation, whereas the second, more mature formulation was among the sources of inspiration of the so-called Primitive Ontology (PO) approach to quantum mechanics, an approach inspired to scientific realism. In the first part of the paper it is argued that, contrary to the Bell wishes, the first formulation of the theory fails to be an effective recipe for addressing the ambiguity underlying the standard formulation of quantum mechanics, whereas it is only the second formulation that successfully paves the way to the PO approach. In the second part, I consider how the distinction between the two formulations of the Bell theory of beables fares vis-a-vis the complex relationship between the theory of beables and the details of the PO approach.

20.Large Reconfigurable Quantum Circuits with SPAD Arrays and Multimode Fibers

Authors:Adrian Makowski, Michał Dąbrowski, Ivan Michel Antolovic, Claudio Bruschini, Hugo Defienne, Edoardo Charbon, Radek Lapkiewicz, Sylvain Gigan

Abstract: Reprogrammable linear optical circuits are essential elements of photonic quantum technology implementations. Integrated optics provides a natural platform for tunable photonic circuits, but faces challenges when high dimensions and high connectivity are involved. Here, we implement high-dimensional linear transformations on spatial modes of photons using wavefront shaping together with mode mixing in a multimode fiber, and measure photon correlations using a time-tagging single-photon avalanche diode (SPAD) array. In order to prove the suitability of our approach for quantum technologies we demonstrate two-photon interferences in a tunable complex linear network -- a generalization of a Hong-Ou-Mandel interference to 22 output ports. We study the scalability of our approach by quantifying the similarity between the ideal photon correlations and the correlations obtained experimentally for various linear transformations. Our results demonstrate the potential of wavefront shaping in complex media in conjunction with SPAD arrays for implementing high-dimensional reconfigurable quantum circuits. Specifically, we achieved $(80.5 \pm 6.8)\%$ similarity for indistinguishable photon pairs and $(84.9 \pm 7.0)\%$ similarity for distinguishable photon pairs using 22 detectors and random circuits. These results emphasize the scalability and reprogrammable nature of our approach.

21.Linear Ultrastrong Optomechanical Interaction

Authors:Kahan Dare, Jannek J. Hansen, Iurie Coroli, Aisling Johnson, Markus Aspelmeyer, Uroš Delić

Abstract: Light-matter interaction in the ultrastrong coupling regime can be used to generate exotic ground states with two-mode squeezing and may be of use for quantum enhanced sensing. Current demonstrations of ultrastrong coupling have been performed in fundamentally nonlinear systems. We report a cavity optomechanical system that operates in the linear coupling regime, reaching a maximum coupling of $g_x/\Omega_x=0.55\pm 0.02$. Such a system is inherently unstable, which may in the future enable strong mechanical squeezing.

22.High-dimensional quantum correlation measurements with an adaptively gated hybrid single-photon camera

Authors:Sanjukta Kundu, Jerzy Szuniewicz, Grzegorz Firlik, Alexander Krupinski-Ptaszek, Radek Lapkiewicz

Abstract: Efficient measurement of high-dimensional quantum correlations, especially spatial ones, is essential for quantum technologies, given their inherent high dimensionality and easy manipulation with basic optical elements. We propose and demonstrate an adaptively-gated hybrid intensified camera (HIC) that combines the information from a high spatial resolution sensor and a high temporal resolution detector, offering precise control over the number of photons detected within each frame. The HIC facilitates spatially resolved single-photon counting measurements. We study the measurement of momentum correlations of photon pairs generated in type-I spontaneous parametric down-conversion with the HIC and demonstrate the possibility of time-tagging the registered photons. With a spatial resolution of nearly 9 megapixels and nanosecond temporal resolution, this system allows for the realization of previously infeasible quantum optics experiments.

23.Niobium Quantum Interference Microwave Circuits with Monolithic Three-Dimensional (3D) Nanobridge Junctions

Authors:Kevin Uhl, Daniel Hackenbeck, Janis Peter, Reinhold Kleiner, Dieter Koelle, Daniel Bothner

Abstract: Nonlinear microwave circuits are key elements for many groundbreaking research directions and technologies, such as quantum computation and quantum sensing. The majority of microwave circuits with Josephson nonlinearities to date is based on aluminum thin films, and therefore they are severely restricted in their operation range regarding temperatures and external magnetic fields. Here, we present the realization of superconducting niobium microwave resonators with integrated, three-dimensional (3D) nanobridge-based superconducting quantum interference devices. The 3D nanobridges (constriction weak links) are monolithically patterned into pre-fabricated microwave LC circuits using neon ion beam milling, and the resulting quantum interference circuits show frequency tunabilities, flux responsivities and Kerr nonlinearities on par with comparable aluminum nanobridge devices, but with the perspective of a much larger operation parameter regime. Our results reveal great potential for application of these circuits in hybrid systems with e.g. magnons and spin ensembles or in flux-mediated optomechanics.

24.Boundary Strong Zero Modes

Authors:Christopher T. Olund, Norman Y. Yao, Jack Kemp

Abstract: Strong zero modes are edge-localized degrees of freedom capable of storing information at infinite temperature, even in systems with no disorder. To date, their stability has only been systematically explored at the physical edge of a system. Here, we extend the notion of strong zero modes to the boundary between two systems, and present a unifying framework for the stability of these boundary strong zero modes. Unlike zero-temperature topological edge modes, which are guaranteed to exist at the interface between a trivial and topological phase, the robustness of boundary strong zero modes is significantly more subtle. This subtlety is perhaps best illustrated by the following dichotomy: we find that the interface between a trivial and ordered phase does not guarantee the existence of a strong zero mode, while the interface between two ordered phases can, in certain cases, lead to an exact strong zero mode.

25.Quantum 3.0: Quantum Learning, Quantum Heuristics and Beyond

Authors:Mrittunjoy Guha Majumdar

Abstract: Quantum learning paradigms address the question of how best to harness conceptual elements of quantum mechanics and information processing to improve operability and functionality of a computing system for specific tasks through experience. It is one of the fastest evolving framework, which lies at the intersection of physics, statistics and information processing, and is the next frontier for data sciences, machine learning and artificial intelligence. Progress in quantum learning paradigms is driven by multiple factors: need for more efficient data storage and computational speed, development of novel algorithms as well as structural resonances between specific physical systems and learning architectures. Given the demand for better computation methods for data-intensive processes in areas such as advanced scientific analysis and commerce as well as for facilitating more data-driven decision-making in education, energy, marketing, pharmaceuticals and health-care, finance and industry.

26.Extending the Computational Reach of a Superconducting Qutrit Processor

Authors:Noah Goss, Samuele Ferracin, Akel Hashim, Arnaud Carignan-Dugas, John Mark Kreikebaum, Ravi K. Naik, David I. Santiago, Irfan Siddiqi

Abstract: Quantum computing with qudits is an emerging approach that exploits a larger, more-connected computational space, providing advantages for many applications, including quantum simulation and quantum error correction. Nonetheless, qudits are typically afflicted by more complex errors and suffer greater noise sensitivity which renders their scaling difficult. In this work, we introduce techniques to tailor and mitigate arbitrary Markovian noise in qudit circuits. We experimentally demonstrate these methods on a superconducting transmon qutrit processor, and benchmark their effectiveness for multipartite qutrit entanglement and random circuit sampling, obtaining up to 3x improvement in our results. To the best of our knowledge, this constitutes the first ever error mitigation experiment performed on qutrits. Our work shows that despite the intrinsic complexity of manipulating higher-dimensional quantum systems, noise tailoring and error mitigation can significantly extend the computational reach of today's qudit processors.

1.Quantitative Relations Between Different Measurement Contexts

Authors:Ming Ji, Holger F. Hofmann

Abstract: In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts can thus be characterized by the inner products of nonorthogonal states in that Hilbert space. Here, we use measurement outcomes that are shared by different contexts to derive specific quantitative relations between the inner products of the Hilbert space vectors that represent the different contexts. It is shown that the probabilities that describe the paradoxes of quantum contextuality can be derived from a very small number of inner products, demonstrating that quantum contextuality is a necessary consequence of the quantitative relations between Hilbert space vectors representing different measurement contexts. The application of our analysis to a product space of two systems reveals that the non-locality of quantum entanglement can be traced back to a local inner product representing the relation between measurement contexts in only one system. Our results thus indicate that the essential non-classical features of quantum mechanics can all be derived systematically from the quantitative relations between different measurement contexts described by the Hilbert space formalism.

2.An optimal sensing protocol for statistically polarized nano-NMR with NV centers

Authors:Nicolas Staudenmaier, Anjusha Vijayakumar-Sreeja, Genko Genov, Daniel Cohen, Christoph Findler, Johannes Lang, Alex Retzker, Fedor Jelezko, Santiago Oviedo-Casado

Abstract: Diffusion noise represents a major constraint to successful liquid state nano-NMR spectroscopy. Using the Fisher information as a faithful measure, we calculate theoretically and show experimentally that phase sensitive protocols are superior in most experimental scenarios, as they maximize information extraction from correlations in the sample. We derive the optimal experimental parameters for quantum heterodyne detection and present the most accurate statistically polarized nano-NMR Qdyne experiments to date, leading the way to resolve chemical shifts and $J$-couplings at the nano-scale.

3.Quantum cyclic redundancy check codes

Authors:Ricard Vilar, Simeon Ball

Abstract: We extend the idea of classical cyclic redundancy check codes to quantum cyclic redundancy check codes. This allows us to construct codes quantum stabiliser codes which can correct burst errors where the burst length attains the quantum Reiger bound. We then consider a certain family of quantum cyclic redundancy check codes for which we present a fast linear time decoding algorithm.

4.Optical self-cooling of a membrane oscillator in a cavity optomechanical experiment at room temperature

Authors:P. Vezio, M. Bonaldi, A. Borrielli, F. Marino, B. Morana, P. M. Sarro, E. Serra, F. Marin

Abstract: Thermal noise is a major obstacle to observing quantum behavior in macroscopic systems. To mitigate its effect, quantum optomechanical experiments are typically performed in a cryogenic environment. However, this condition represents a considerable complication in the transition from fundamental research to quantum technology applications. It is therefore interesting to explore the possibility of achieving the quantum regime in room temperature experiments. In this work we test the limits of sideband cooling vibration modes of a SiN membrane in a cavity optomechanical experiment. We obtain an effective temperature of a few mK, corresponding to a phononic occupation number of around 100. We show that further cooling is prevented by the excess classical noise of our laser source, and we outline the road toward the achievement of ground state cooling

5.Creation of NV centers in diamond under 155 MeV electron irradiation

Authors:Elena Losero, Valentin Goblot, Yuchun Zhu, Hossein Babashah, Victor Boureau, Florian Burkart, Christophe Galland

Abstract: Single-crystal diamond substrates presenting a high concentration of negatively charged nitrogen-vacancy centers (NV-) are on high demand for the development of optically pumped solid-state sensors such as magnetometers, thermometers or electrometers. While nitrogen impurities can be easily incorporated during crystal growth, the creation of vacancies requires further treatment. Electron irradiation and annealing is often chosen in this context, offering advantages with respect to irradiation by heavier particles that negatively affect the crystal lattice structure and consequently the NV- optical and spin properties. A thorough investigation of electron irradiation possibilities is needed to optimize the process and improve the sensitivity of NV-based sensors. In this work we examine the effect of electron irradiation in a previously unexplored regime: extremely high energy electrons, at 155 MeV. We develop a simulation model to estimate the concentration of created vacancies and experimentally demonstrate an increase of NV- concentration by more than 3 orders of magnitude following irradiation of a nitrogen-rich HPHT diamond over a very large sample volume, which translates into an important gain in sensitivity. Moreover, we discuss the impact of electron irradiation in this peculiar regime on other figures of merits relevant for NV sensing, i.e. charge state conversion efficiency and spin relaxation time. Finally, the effect of extremely high energy irradiation is compared with the more conventional low energy irradiation process, employing 200 keV electrons from a transmission electron microscope, for different substrates and irradiation fluences, evidencing sixty-fold higher yield of vacancy creation per electron at 155 MeV.

6.Experimental Verification of Many-Body Entanglement Using Thermodynamic Quantities

Authors:Jitendra Joshi, Mir Alimuddin, T S Mahesh, Manik Banik

Abstract: The phenomenon of quantum entanglement underlies several important protocols that enable emerging quantum technologies. Being an extremely delicate resource entangled states easily get perturbed by their external environment, and thus makes the question of entanglement certification immensely crucial for successful implementation of the protocols involving entanglement. In this work, we propose a set of entanglement criteria for multi-qubit systems that can be easily verified by measuring certain thermodynamic quantities. In particular, the criteria depend on the difference in optimal works extractable from an isolated quantum system under global and local interactions, respectively. As a proof of principle, we demonstrate the proposed thermodynamic criteria on nuclear spin registers of up to 10 qubits using Nuclear Magnetic Resonance architecture. We prepare noisy Greenberger-Horne-Zeilinger class of states in star-topology systems and certify their entanglement through our proposed criteria. We also provide elegant means of entanglement certification in many-body systems when only partial or even no knowledge about the state is available.

7.Modifying $n$-qubit controlled-$ZX$ gate to be $n$-qubit Toffoli gate

Authors:Jian Leng, Fan Yang, Xiang-Bin Wang

Abstract: The decomposition for controlled-$ZX$ gate in [Phys. Rev. A, 87, 062318 (2013)] has a shallow circuit depth $8n-20$ with no ancilla. Here we modify this decomposition to decompose $n$-qubit Toffoli gate with only $2n-3$ additional single-qubit gates. The circuit depth is unchanged and no ancilla is needed. We explicitly show that the circuit after decomposition can be easily constructed in present physical systems.

8.Robustness of Quantum Random Walk Search Algorithm in Hypercube when only first or both first and second neighbors are measured

Authors:Hristo Tonchev, Petar Danev

Abstract: In this work we study the robustness of two modifications of quantum random walk search algorithm on hypercube. In the first previously suggested modification, on each even iteration only quantum walk is applied. And in the second, the closest neighbors of the solution are measured classically. In our approach the traversing coin is constructed by both generalized Householder reflection and an additional phase multiplier and we investigate the stability of the algorithm to deviations in those phases. We have shown that the unmodified algorithm becomes more robust when a certain relation between those phases is preserved. The first modification we study here does not lead to any change in the robustness of quantum random walk search algorithm. However, when a measurement of the first and second neighbors is included, there are some differences. The most important one, in view of our study of the robustness, is an increase in the stability of the algorithm, especially for large coin dimensions.

9.First detection probability in quantum resetting via random projective measurements

Authors:Manas Kulkarni, Satya N. Majumdar

Abstract: We provide a general framework to compute the probability distribution $F_r(t)$ of the first detection time of a 'state of interest' in a generic quantum system subjected to random projective measurements. In our 'quantum resetting' protocol, resetting of a state is not implemented by an additional classical stochastic move, but rather by the random projective measurement. We then apply this general framework to Poissoinan measurement protocol with a constant rate $r$ and demonstrate that exact results for $F_r(t)$ can be obtained for a generic two level system. Interestingly, the result depends crucially on the detection schemes involved and we have studied two complementary schemes, where the state of interest either coincides or differs from the initial state. We show that $F_r(t)$ at short times vanishes universally as $F_r(t)\sim t^2$ as $t\to 0$ in the first scheme, while it approaches a constant as $t\to 0$ in the second scheme. The mean first detection time, as a function of the measurement rate $r$, also shows rather different behaviors in the two schemes. In the former, the mean detection time is a nonmonotonic function of $r$ with a single minimum at an optimal value $r^*$, while in the later, it is a monotonically decreasing function of $r$, signalling the absence of a finite optimal value. These general predictions for arbitrary two level systems are then verified via explicit computation in the Jaynes-Cummings model of light-matter interaction. We also generalise our results to non-Poissonian measurement protocols with a renewal structure where the intervals between successive independent measurements are distributed via a general distribution $p(\tau)$ and show that the short time behavior of $F_r(t)\sim p(0)\, t^2$ is universal as long as $p(0)\ne 0$. This universal $t^2$ law emerges from purely quantum dynamics that dominates at early times.

10.Dopant-assisted stabilization of negatively charged single nitrogen-vacancy centers in phosphorus-doped diamond at low temperatures

Authors:Jianpei Geng, Tetyana Shalomayeva, Mariia Gryzlova, Amlan Mukherjee, Santo Santonocito, Dzhavid Dzhavadzade, Durga Dasari, Hiromitsu Kato, Rainer Stöhr, Andrej Denisenko, Norikazu Mizuochi, Jörg Wrachtrup

Abstract: Charge state instabilities have been a bottleneck for the implementation of solid-state spin systems and pose a major challenge to the development of spin-based quantum technologies. Here we investigate the stabilization of negatively charged nitrogen-vacancy (NV$^-$) centers in phosphorus-doped diamond at liquid helium temperatures. Photoionization of phosphorous donors in conjunction with charge diffusion at the nanoscale enhances NV$^0$ to NV$^-$ conversion and stabilizes the NV$^-$ charge state without the need for an additional repump laser. The phosphorus-assisted stabilization is explored and confirmed both with experiments and our theoretical model. Stable photoluminescence-excitation spectra are obtained for NV$^-$ centers created during the growth. The fluorescence is continuously recorded under resonant excitation to real-time monitor the charge state and the ionization and recombination rates are extracted from time traces. We find a linear laser power dependence of the recombination rate as opposed to the conventional quadratic dependence, which is attributed to the photo-ionization of phosphorus atoms.

11.Parameter Setting in Quantum Approximate Optimization of Weighted Problems

Authors:Shree Hari Sureshbabu, Dylan Herman, Ruslan Shaydulin, Joao Basso, Shouvanik Chakrabarti, Yue Sun, Marco Pistoia

Abstract: Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate algorithm for solving combinatorial optimization problems on quantum computers. However, in many cases QAOA requires computationally intensive parameter optimization. The challenge of parameter optimization is particularly acute in the case of weighted problems, for which the eigenvalues of the phase operator are non-integer and the QAOA energy landscape is not periodic. In this work, we develop parameter setting heuristics for QAOA applied to a general class of weighted problems. First, we derive optimal parameters for QAOA with depth $p=1$ applied to the weighted MaxCut problem under different assumptions on the weights. In particular, we rigorously prove the conventional wisdom that in the average case the first local optimum near zero gives globally-optimal QAOA parameters. Second, for $p\geq 1$ we prove that the QAOA energy landscape for weighted MaxCut approaches that for the unweighted case under a simple rescaling of parameters. Therefore, we can use parameters previously obtained for unweighted MaxCut for weighted problems. Finally, we prove that for $p=1$ the QAOA objective sharply concentrates around its expectation, which means that our parameter setting rules hold with high probability for a random weighted instance. We numerically validate this approach on general weighted graphs and show that on average the QAOA energy with the proposed fixed parameters is only $1.1$ percentage points away from that with optimized parameters. Third, we propose a general heuristic rescaling scheme inspired by the analytical results for weighted MaxCut and demonstrate its effectiveness using QAOA with the XY Hamming-weight-preserving mixer applied to the portfolio optimization problem. Our heuristic improves the convergence of local optimizers, reducing the number of iterations by 7.2x on average.

12.Universal limit on spatial quantum superpositions with massive objects due to phonons

Authors:Carsten Henkel, Ron Folman

Abstract: The superposition principle is one of the founding principles of quantum theory. Spatial quantum superpositions have so far been tested only with small systems, from photons and elementary particles to atoms and molecules. Such superpositions for massive objects have been a long-standing sought-after goal. This is important not only in order to confirm quantum theory in new regimes, but also in order to probe the quantum-gravity interface. In addition, such an experiment will enable to test exotic theories, and may even enable new technology. Creating such superpositions is notoriously hard because of environmental decoherence, whereby the large object couples strongly to the environment which turns the delicate quantum state into a statistical mixture (classical state). However, advances in the technology of isolation could in future suppress such decoherence. Here we present a decoherence channel which is not external but internal to the object, and consequently improved isolation would not help. This channel originates from the phonons (sound waves) within the object. We show that such phonons are excited as part of any splitting process, and thus we establish a fundamental and universal limit on the possibility of future spatial quantum superpositions with massive objects.

13.Defining a quantum active particle using non-Hermitian quantum walk

Authors:Manami Yamagishi, Naomichi Hatano, Hideaki Obuse

Abstract: The main aim of the present paper is to define an active matter in a quantum framework and investigate difference and commonalities of quantum and classical active matters. Although the research field of active matter has been expanding wider and wider, most research is conducted in classical systems; on the contrary, there is no universal theoretical framework for quantum active matter. We here propose a truly quantum active-matter model with a non-Hermitian quantum walk and show numerical results in one- and two-dimensional systems. We aim to reproduce similar results that Schweitzer \textit{et al.} obtained with their classical active Brownian particle; that is, the Brownian particle, with a finite energy take-up, becomes active and climbs up a potential wall. We realize such a system with non-Hermitian quantum walks. We introduce new internal states, the ground state and the excited state, and a new non-Hermitian operator $N(g)$ for an asymmetric transition between both states. The non-Hermiticity parameter $g$ promotes transition to the excited state and hence the particle takes up energy from the environment. We realize a system without momentum conservation by manipulating a parameter $\theta$ for the coin operator for a discrete-time quantum walk; we utilize the property that the continuum limit of a one-dimensional discrete-time quantum walk gives the Dirac equation with its mass proportional to the parameter $\theta$. With our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a non-trivial way as we increase the non-Hermiticity parameter $g$, which is similar to the classical active Brownian particle. Meanwhile, we also observe unique features of quantum walks, namely, ballistic propagation of peaks (1D) and the walker staying on the constant energy plane (2D).

14.Learning t-doped stabilizer states

Authors:Lorenzo Leone, Salvatore F. E. Oliviero, Alioscia Hamma

Abstract: In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number t of non-Clifford gates. To tackle this problem, we introduce a novel algebraic framework for t-doped stabilizer states by utilizing tools from stabilizer entropy. Leveraging this new structure, we develop an algorithm that uses sampling from the distribution obtained by squaring expectation values of Pauli operators that can be obtained by Bell sampling on the state and its conjugate in the computational basis. The algorithm requires resources of complexity $O(\exp(t)\poly(n))$ and exhibits an exponentially small probability of failure.

1.Complete spectral characterization of biphotons by simultaneously determining its frequency sum and difference in a single quantum interferometer

Authors:Baihong Li, Changhua Chen, Boxin Yuan, Xiangying Hao, Rui-Bo Jin

Abstract: We theoretically propose a novel quantum interferometer in which the NOON state interferometer (NOONI) is combined with the Hong-Ou-Mandel interferometer (HOMI). This interferometer combined the advantages of both the NOONI that depends on biphoton frequency sum, and the HOMI that depends on biphoton frequency difference into a single interferometer. It can thus simultaneously obtain the spectral correlation information of biphotons in both frequency sum and difference by taking the Fourier transform from a single time-domain quantum interferogram, which provides a method for complete spectral characterization of an arbitrary two-photon state with exchange symmetry. A direct application of such an interferometer can be found in quantum Fourier-transform spectroscopy where direct spectral measurement is difficult. Furthermore, as it can realize the measurement of time intervals on three scales at the same time, we expect that it can provide a new method in quantum metrology. Finally, we discuss another potential application of such an interferometer in the generation and characterization of high-dimensional and phase-controlled frequency entanglement.

2.Co-propagation of 6 Tb/s (60*100Gb/s) DWDM & QKD channels with ~17 dBm aggregated WDM power over 50 km standard single mode fiber

Authors:P. Gavignet, F. Mondain, E. Pincemin, A. J. Grant, L. Johnson, R. I. Woodward, J. F. Dynes, A. J. Shields

Abstract: We report the co-propagation, over 50 km of SSMF, of the quantum channel (1310 nm) of a QKD system with ~17 dBm total power of DWDM data channels (1550 nm range). A metric to evaluate Co-propagation Efficiency is proposed.

3.Tuning atom-field interaction via phase shaping

Authors:Y. -T. Cheng, C. -H. Chien, K. -M. Hsieh, Y. -H. Huang, P. Y. Wen, W. -J. Lin, Y. Lu, F. Aziz, C. -P. Lee, K. -T. Lin, C. -Y. Chen, J. C. Chen, C. -S. Chuu, A. F. Kockum, G. -D. Lin, Y. -H. Lin, I. -C. Hoi

Abstract: A coherent electromagnetic field can be described by its amplitude, frequency, and phase. All these properties can influence the interaction between the field and an atom. Here we demonstrate the phase shaping of microwaves that are loaded onto a superconducting artificial atom in a semiinfinite 1D transmission line, a setup corresponding to an atom in front of a mirror. In particular, we input a weak exponentially rising pulse with phase modulation to the atom-mirror system. We observe that field-atom interaction can be tuned from nearly full interaction (loading efficiency, i.e., amount of energy transferred from the field to the atom, of 94.5 %) to effectively no interaction (loading efficiency 3.5 %).

4.Layer-by-layer disentangling two-dimensional topological quantum codes

Authors:Mohammad Hossein Zarei, Mohsen Rahmani Haghighi

Abstract: While local unitary transformations are used for identifying quantum states which are in the same topological class, non-local unitary transformations are also important for studying the transition between different topological classes. In particular, it is an important task to find suitable non-local transformations that systematically sweep different topological classes. Here, regarding the role of dimension in the topological classes, we introduce partially local unitary transformations namely Greenberger-Horne-Zeilinger (GHZ) disentanglers which reduce the dimension of the initial topological model by a layer-by-layer disentangling mechanism. We apply such disentanglers to two-dimensional (2D) topological quantum codes and show that they are converted to many copies of Kitaev's ladders. It implies that the GHZ disentangler causes a transition from an intrinsic topological phase to a symmetry-protected topological phase. Then, we show that while Kitaev's ladders are building blocks of both color code and toric code, there are different patterns of entangling ladders in 2D color code and toric code. It shows that different topological features of these topological codes are reflected in different patterns of entangling ladders. In this regard, we propose that the layer-by-layer disentangling mechanism can be used as a systematic method for classification of topological orders based on finding different patterns of the long-range entanglement in topological lattice models.

5.Comment on "Weak values and the past of a quantum particle"

Authors:Lev Vaidman

Abstract: In a recent paper, Hance, Rarity and Ladyman [Phys. Rev. Res. {\bf 5}, 023048 (2023)] criticized recent proposals connecting weak values and the past of a quantum particle. I argue that their conclusion follows from a conceptual error in understanding the approach to the past of the particle they discuss.

6.Practical Phase-Coding Side-Channel-Secure Quantum Key Distribution

Authors:Yang-Guang Shan, Zhen-Qiang Yin, Shuang Wang, Wei Chen, De-Yong He, Guang-Can Guo, Zheng-Fu Han

Abstract: All kinds of device loopholes give rise to a great obstacle to practical secure quantum key distribution (QKD). In this article, inspired by the original side-channel-secure protocol [Physical Review Applied 12, 054034 (2019)], a new QKD protocol called phase-coding side-channel-secure (PC-SCS) protocol is proposed. This protocol can be immune to all uncorrelated side channels of the source part and all loopholes of the measurement side. A finite-key security analysis against coherent attack of the new protocol is given. The proposed protocol only requires modulation of two phases, which can avoid the challenge of preparing perfect vacuum states. Numerical simulation shows that a practical transmission distance of 300 km can be realized by the PC-SCS protocol.

7.Open system approach to Neutrino oscillations in a quantum walk framework

Authors:Himanshu Sahu, C. M. Chandrashekar

Abstract: Quantum simulation provides a computationally-feasible approach to model and study many problems in chemistry, condensed-matter physics, or high-energy physics where quantum phenomenon define the systems behaviour. In high-energy physics, quite a few possible applications are investigated in the context of gauge theories and their application to dynamic problems, topological problems, high-baryon density configurations, or collective neutrino oscillations. In particular, schemes for simulating neutrino oscillations are proposed using a quantum walk framework. In this study, we approach the problem of simulating neutrino oscillation from the perspective of open quantum systems by treating the position space of quantum walk as environment. We have obtained the recurrence relation for Kraus operator which is used to represent the dynamics of the neutrino flavor change in the form of reduced coin states. We establish a connection between the dynamics of reduced coin state and neutrino phenomenology, enabling one to fix the simulation parameters for a given neutrino experiment and reduces the need for extended position space to simulate neutrino oscillations. We have also studied the behavior of linear entropy as a measure of entanglement between different flavors in the same framework.

8.Liouville Space Neural Network Representation of Density Matrices

Authors:Simon Kothe, Peter Kirton

Abstract: Neural network quantum states as ansatz wavefunctions have shown a lot of promise for finding the ground state of spin models. Recently, work has been focused on extending this idea to mixed states for simulating the dynamics of open systems. Most approaches so far have used a purification ansatz where a copy of the system Hilbert space is added which when traced out gives the correct density matrix. Here, we instead present an extension of the Restricted Boltzmann Machine which directly represents the density matrix in Liouville space. This allows the compact representation of states which appear in mean-field theory. We benchmark our approach on two different version of the dissipative transverse field Ising model which show our ansatz is able to compete with other state-of-the-art approaches.

9.Gauge dependence of the Aharonov-Bohm phase in quantum electrodynamics framework

Authors:A. Hayashi

Abstract: The Aharonov-Bohm (AB) phase is usually associated with a line integral of the electromagnetic vector potential generated by an external current source, such as a solenoid. According to this interpretation, the AB phase of a nonclosed path cannot be observed, as the integral depends on the gauge choice of the vector potential. Recent attempts to explain the AB effect through the interaction between a charged particle and an external current, mediated by the exchange of quantum photons, have assumed that the AB phase shift is proportional to the change in interaction energy between the charged particle and the external current source. As a result, these attempts argue that the AB phase change along a path does not depend on the gauge choice, and that the AB phase shift for a nonclosed path is in principle measurable. In this paper, we critically examine this claim and demonstrate that the phase obtained through this approach is actually gauge-dependent and not an observable for a nonclosed path. We also provide a brief critical discussion of the proposed experiment for observing the AB phase shift of a nonclosed path.

10.Device-independent randomness based on a tight upper bound of the maximal quantum value of chained inequality

Authors:Youwang Xiao, Xinhui Li, Jing Wang, Ming Li, Shao-Ming Fei

Abstract: The violation of Bell inequality not only provides the most radical departure of quantum theory from classical concepts, but also paves the way of applications in such as device independent randomness certification. Here, we derive the tight upper bound of the maximum quantum value for chained Bell inequality with arbitrary number of measurements on each party. \lxh{ The constraints where the upper bound saturates are also presented. This method provides us the necessary and sufficient conditions for some quantum states to violate the chained Bell inequality with arbitrary number of measurements}. Based on the tight upper bound we present the lower bounds on the device independent randomness with respect to the Werner states. \lxh{In particular, we present lower bounds on the randomness generation rates of chained Bell inequality for different number of measurements, which are compared with the family of Bell inequalities proposed by Wooltorton et al. [Phys. Rev. Lett. 129, 150403 (2022)]. Our results show that chained Bell inequality with three measurements has certain advantages at a low level of noise and could be used to improve randomness generation rates in practice.

11.Information Theoretic Significance of Projective Measurements

Authors:Huangjun Zhu

Abstract: Projective measurements in quantum theory have a very simple algebraic definition, but their information theoretic significance is quite elusive. Here we introduce a simple order relation based on the concentration of Fisher information, which complements the familiar data-processing order. Under this order relation, the information theoretic significance of projective measurements stands out immediately. Notably, projective measurements are exactly those quantum measurements whose extracted Fisher information is as concentrated as possible, which we call Fisher-sharp measurements. We also introduce the concept of sharpness index and show that it is completely determined by the finest projective measurement among the coarse graining of a given measurement.

12.Semi-device independent nonlocality certification for near-term quantum networks

Authors:Sophie Engineer, Ana C. S. Costa, Alexandre C. Orthey Jr., Xiaogang Qiang, Jianwei Wang, Jeremy L. O'Brien, Jonathan C. F. Matthews, Will McCutcheon, Roope Uola, Sabine Wollmann

Abstract: Verifying entanglement between parties is essential for creating a secure quantum network, and Bell tests are the most rigorous method for doing so. However, if there is any signaling between the parties, then the violation of these inequalities can no longer be used to draw conclusions about the presence of entanglement. This is because signaling between the parties allows them to coordinate their measurement settings and outcomes, which can give rise to a violation of Bell inequalities even if the parties are not genuinely entangled. There is a pressing need to examine the role of signaling in quantum communication protocols from multiple perspectives, including communication security, physics foundations, and resource utilization while also promoting innovative technological applications. Here, we propose a semi-device independent protocol that allows us to numerically correct for effects of correlations in experimental probability distributions, caused by statistical fluctuations and experimental imperfections. Our noise robust protocol presents a relaxation of a tomography-based optimisation method called the steering robustness, that uses semidefinite programming to numerically identify the optimal quantum steering inequality without the need for resource-intensive tomography. The proposed protocol is numerically and experimentally analyzed in the context of random, misaligned measurements, correcting for signalling where necessary, resulting in a higher probability of violation compared to existing state-of-the-art inequalities. Our work demonstrates the power of semidefinite programming for entanglement verification and brings quantum networks closer to practical applications.

13.Anonymous estimation of intensity distribution of magnetic fields with quantum sensing network

Authors:Hiroto Kasai, Yuki Takeuchi, Yuichiro Matsuzaki, Yasuhiro Tokura

Abstract: A quantum sensing network is used to simultaneously detect and measure physical quantities, such as magnetic fields, at different locations. However, there is a risk that the measurement data is leaked to the third party during the communication. Many theoretical and experimental efforts have been made to realize a secure quantum sensing network where a high level of security is guaranteed. In this paper, we propose a protocol to estimate statistical quantities of the target fields at different places without knowing individual value of the target fields. We generate an enanglement between $L$ quantum sensors, let the quantum sensor interact with local fields, and perform specific measurements on them. By calculating the quantum Fisher information to estimate the individual value of the magnetic fields, we show that we cannot obtain any information of the value of the individual fields in the limit of large $L$. On the other hand, in our protocol, we can estimate theoretically any moment of the field distribution by measuring a specific observable and evaluated relative uncertainty of $k$-th ($k=1,2,3,4$) order moment. Our results are a significant step towards using a quantum sensing network with security inbuilt.

14.Variational quantum algorithms on cat qubits

Authors:Anne-Solène Bornens, Michel Nowak

Abstract: Variational Quantum Algorithms (VQA) have emerged with a wide variety of applications. One question to ask is either they can efficiently be implemented and executed on existing architectures. Current hardware suffers from uncontrolled noise that can alter the expected results of one calculation. The nature of this noise is different from one technology to another. In this work, we chose to investigate a technology that is intrinsically resilient to bit-flips: cat qubits. To this end, we implement two noise models. The first one is hardware-agnostic -- in the sense that it is used in the literature to cover different hardware types. The second one is specific to cat qubits. We perform simulations on two types of problems that can be formulated with VQAs (Quantum Approximate Optimization Algorithm (QAOA) and the Variatinoal Quantum Linear Soler (VQLS)), study the impact of noise on the evolution of the cost function and extract noise level thresholds from which a noise-resilient regime can be considered. By tackling compilation issues, we discuss the need of implementing hardware-specific noise models as hardware-agnostic ones can lead to misleading conclusions regarding the regime of noise that is acceptable for an algorithm to run.

15.Distributing circuits over heterogeneous, modular quantum computing network architectures

Authors:Pablo Andres-Martinez, Tim Forrer, Daniel Mills, Jun-Yi Wu, Luciana Henaut, Kentaro Yamamoto, Mio Murao, Ross Duncan

Abstract: We consider a heterogeneous network of quantum computing modules, sparsely connected via Bell states. Operations across these connections constitute a computational bottleneck and they are likely to add more noise to the computation than operations performed within a module. We introduce several techniques for transforming a given quantum circuit into one implementable on a network of the aforementioned type, minimising the number of Bell states required to do so. We extend previous works on circuit distribution over fully connected networks to the case of heterogeneous networks. On the one hand, we extend the hypergraph approach of [Andres-Martinez & Heunen. 2019] to arbitrary network topologies. We additionally make use of Steiner trees to find efficient realisations of the entanglement sharing within the network, reusing already established connections as often as possible. On the other hand, we extend the embedding techniques of [Wu, et al. 2022] to networks with more than two modules. Furthermore, we discuss how these two seemingly incompatible approaches can be made to cooperate. Our proposal is implemented and benchmarked; the results confirming that, when orchestrated, the two approaches complement each other's weaknesses.

16.Site-Selective Enhancement of Superconducting Nanowire Single-Photon Detectors via Local Helium Ion Irradiation

Authors:Stefan Strohauer, Fabian Wietschorke, Lucio Zugliani, Rasmus Flaschmann, Christian Schmid, Stefanie Grotowski, Manuel Müller, Björn Jonas, Matthias Althammer, Rudolf Gross, Kai Müller, Jonathan J. Finley

Abstract: Achieving homogeneous performance metrics between nominally identical pixels is challenging for the operation of arrays of superconducting nanowire single-photon detectors (SNSPDs). Here, we utilize local helium ion irradiation to post-process and tune single-photon detection efficiency, switching current, and critical temperature of individual devices on the same chip. For 12nm thick highly absorptive SNSPDs, which are barely single-photon sensitive prior to irradiation, we observe an increase of the system detection efficiency from $< 0.05\,\%$ to $(55.3 \pm 1.1)\,\%$ following irradiation. Moreover, the internal detection efficiency saturates at a temperature of 4.5 K after irradiation with $1800\, \mathrm{ions}\, \mathrm{nm}^{-2}$. For irradiated 10 nm thick detectors we observe a doubling of the switching current (to $20\, \mu\mathrm{A}$) compared to 8 nm SNSPDs of similar detection efficiency, increasing the amplitude of detection voltage pulses. Investigations of the scaling of superconducting thin film properties with irradiation up to a fluence of $2600\, \mathrm{ions}\, \mathrm{nm}^{-2}$ revealed an increase of sheet resistance and a decrease of critical temperature towards high fluences. A physical model accounting for defect generation and sputtering during helium ion irradiation is presented and shows good qualitative agreement with experiments.

17.Controlling quantum chaos: time-dependent kicked rotor

Authors:Steven Tomsovic, Juan Diego Urbina, Klaus Richter

Abstract: One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201 (2023)], a generalization of this targeting method to quantum systems was demonstrated using successive unitary transformations that counter the natural spreading of a quantum state. In this paper further details are given and an important quite general extension is established. In particular, an alternate approach to constructing the coherent control dynamics is given, which introduces a new time-dependent, locally stable control Hamiltonian that continues to use the chaotic heteroclinic orbits previously introduced, but without the need of countering quantum state spreading. Implementing that extension for the quantum kicked rotor generates a much simpler approximate control technique than discussed in the letter, which is a little less accurate, but far more easily realizable in experiments. The simpler method's error can still be made to vanish as $\hbar \rightarrow 0$.

18.NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization

Authors:M. R. Perelshtein, A. I. Pakhomchik, Ar. A. Melnikov, M. Podobrii, A. Termanova, I. Kreidich, B. Nuriev, S. Iudin, C. W. Mansell, V. M. Vinokur

Abstract: Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum algorithms training, the shape of their cost landscape, the accuracy of their output, and their ability to scale to large-size problems. Here, we present an approximate gradient-based quantum algorithm for hardware-efficient circuits with amplitude encoding. We show how simple linear constraints can be directly incorporated into the circuit without additional modification of the objective function with penalty terms. We employ numerical simulations to test it on MaxCut problems with complete weighted graphs with thousands of nodes and run the algorithm on a superconducting quantum processor. We find that for unconstrained MaxCut problems with more than 1000 nodes, the hybrid approach combining our algorithm with a classical solver called CPLEX can find a better solution than CPLEX alone. This demonstrates that hybrid optimization is one of the leading use cases for modern quantum devices.

19.Bipartite entanglement detection by local generalized measurements

Authors:Maximilian Schumacher, Gernot Alber

Abstract: Entanglement detection by local measurements, which can possibly be performed by far distant observers, are of particular interest for applications in quantum key distribution and quantum communication. In this paper sufficient conditions for arbitrary dimensional bipartite entanglement detection based on correlation matrices and joint probability distributions of such local measurements are investigated. In particular, their dependence on the nature of the local measurements is explored for typical bipartite quantum states and for measurements involving local orthonormal hermitian operators bases (LOOs) or generalized measurements based on informationally complete positive operator valued measures of the recently introduced $(N,M)$-type ($(N,M)$-POVMs) \cite{NMPOVM}. It is shown that symmetry properties of $(N,M)$-POVMs imply that sufficient conditions for bipartite entanglement detection exhibit peculiar scaling properties relating different equally efficient local entanglement detection scenarios. For correlation-matrix based bipartite local entanglement detection, for example, this has the consequence that LOOs and all informationally complete $(N,M)$-POVMs are equally powerful. With the help of a hit-and-run Monte-Carlo algorithm the effectiveness of local entanglement detection of typical bipartite quantum states is explored numerically. For this purpose Euclidean volume ratios between locally detectable entangled states and all bipartite quantum states are determined.

20.Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States

Authors:Yuchen Guo, Jian-Hao Zhang, Zhen Bi, Shuo Yang

Abstract: We investigate the phase diagram at the boundary of an infinite two-dimensional cluster state subject to bulk measurements using tensor network methods. The state is subjected to uniform measurements $M = \cos{\theta}Z+\sin{\theta}X$ on the lower boundary qubits and all bulk qubits. Our results show that the boundary of the system exhibits volume-law entanglement at the measurement angle $\theta = \pi/2$ and area-law entanglement for any $\theta < \pi/2$. Within the area-law phase, a phase transition occurs at $\theta_c=1.371$. The phase with $\theta \in(\theta_c,\pi/2)$ is characterized by a non-injective matrix product state, which cannot be realized as the unique ground state of a 1D local, gapped Hamiltonian. Instead, it resembles a cat state with spontaneous symmetry breaking. These findings demonstrate that the phase diagram of the boundary of a two-dimensional system can be more intricate than that of a standard one-dimensional system.

21.Paradox with Phase-Coupled Interferometers

Authors:Saba Etezad-Razavi, Lucien Hardy

Abstract: A pair of interferometers can be coupled by allowing one path from each to overlap such that if the particles meet in this overlap region, they annihilate. It was shown by one of us over thirty years ago that such annihilation-coupled interferometers can exhibit apparently paradoxical behaviour. More recently, Bose et al. and Marletto and Vedral have considered a pair of interferometers that are phase-coupled (where the coupling is through gravitational interaction). In this case one path from each interferometer undergoes a phase-coupling interaction. We show that these phase-coupled interferometers exhibit the same apparent paradox as the annihilation-coupled interferometers, though in a curiously dual manner.

22.Quantum Kolmogorov complexity and quantum correlations in deterministic-control quantum Turing machines

Authors:Mariano Lemus, Ricardo Faleiro, Paulo Mateus, Nikola Paunković, André Souto

Abstract: We extend the deterministic-control quantum Turing machine (dcq-TM) model to incorporate mixed state inputs and outputs. Moreover, we define dcq-computable states as those that can be accurately approximated by a dcq-TM, and we introduce (conditional) Kolmogorov complexity of quantum states. We show that this notion is machine independent and that the set of dcq-computable states coincides with states having computable classical representations. Furthermore, we prove an algorithmic information version of the no-cloning theorem stating that cloning most quantum states is as difficult as creating them. Finally, we also propose a correlation-aware definition for algorithmic mutual information and shown that it satisfies symmetry of information property.

23.Experimental quantum channel discrimination using metastable states of a trapped ion

Authors:Kyle DeBry, Jasmine Sinanan-Singh, Colin D. Bruzewicz, David Reens, May E. Kim, Matthew P. Roychowdhury, Robert McConnell, Isaac L. Chuang, John Chiaverini

Abstract: We present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped $^{40}\text{Ca}^{+}$ ion. The three channels cannot be distinguished unambiguously using repeated single channel queries, the natural classical analogue. We develop techniques for using the 6-dimensional $\text{D}_{5/2}$ state space for quantum information processing, and we implement protocols to discriminate quantum channel analogues of phase shift keying and amplitude shift keying data encodings used in classical radio communication. The demonstrations achieve discrimination accuracy exceeding $99\%$ in each case, limited entirely by known experimental imperfections.

24.Error Basis and Quantum Channel

Authors:B. V. Rajarama Bhat, Purbayan Chakraborty, Uwe Franz

Abstract: The Weyl operators give a convenient basis of $M_n(\mathbb{C})$ which is also orthonormal with respect to the Hilbert-Schmidt inner product. The properties of such a basis can be generalised to the notion of a nice error basis(NEB), as introduced by E. Knill. We can use an NEB of $M_n(\mathbb{C})$ to construct an NEB for $Lin(M_n(\mathbb{C}))$, the space of linear maps on $M_n(\mathbb{C})$. Any linear map on $M_n(\mathbb{C})$ will then correspond to a $n^2\times n^2$ coefficient matrix in the basis decomposition with respect to such an NEB of $Lin(M_n(\mathbb{C}))$. Positivity, complete (co)positivity or other properties of a linear map can be characterised in terms of such a coefficient matrix.

25.Robust engineering of maximally entangled states by identical particle interferometry

Authors:Matteo Piccolini, Vittorio Giovannetti, Rosario Lo Franco

Abstract: We propose a procedure for the robust preparation of maximally entangled states of identical fermionic qubits, studying the role played by particle statistics in the process. The protocol exploits externally activated noisy channels to reset the system to a known state. The subsequent interference effects generated at a beam splitter result in a mixture of maximally entangled Bell states and NOON states. We also discuss how every maximally entangled state of two fermionic qubits distributed over two spatial modes can be obtained from one another by fermionic passive optical transformations. Using a pseudospin-insensitive, non-absorbing, parity check detector, the proposed technique is thus shown to deterministically prepare any arbitrary maximally entangled state of two identical fermions. These results extend recent findings related to bosonic qubits. Finally, we analyze the performance of the protocol for both bosons and fermions when the externally activated noisy channels are not used and the two qubits undergo standard types of noise. The results supply further insights towards viable strategies for noise-protected entanglement exploitable in quantum-enhanced technologies.

26.Unique Steady-State Squeezing in a Driven Quantum Rabi Model

Authors:Karol Gietka, Christoph Hotter, Helmut Ritsch

Abstract: Squeezing is essential to many quantum technologies and our understanding of quantum physics. Here we develop a theory of steady-state squeezing that can be generated in the closed and open quantum Rabi as well as Dicke model. To this end, we eliminate the spin dynamics which effectively leads to an abstract harmonic oscillator whose eigenstates are squeezed with respect to the physical harmonic oscillator. The generated form of squeezing has the unique property of time-independent uncertainties and squeezed dynamics, a novel type of quantum behavior. Such squeezing might find applications in continuous back-action evading measurements and should already be observable in optomechanical systems and Coulomb crystals.

27.Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution

Authors:Alessandro Sinibaldi, Clemens Giuliani, Giuseppe Carleo, Filippo Vicentini

Abstract: We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias or exponential sample complexity when the wave function contains some (possibly approximate) zeros, an important case for fermionic systems and quantum information protocols; (ii) show that a different scheme based on the solution of an optimization problem at each time step is free from such problems; (iii) improve the sample complexity of this latter approach by several orders of magnitude with respect to previous proofs of concept. Finally, we apply our advancements to study the high-entanglement phase in a protocol of non-Clifford unitary dynamics with local random measurements in 2D, first benchmarking on small spin lattices and then extending to large systems.

28.A Classical Architecture For Digital Quantum Computers

Authors:Fang Zhang, Xing Zhu, Rui Chao, Cupjin Huang, Linghang Kong, Guoyang Chen, Dawei Ding, Haishan Feng, Yihuai Gao, Xiaotong Ni, Liwei Qiu, Zhe Wei, Yueming Yang, Yang Zhao, Yaoyun Shi, Weifeng Zhang, Peng Zhou, Jianxin Chen

Abstract: Scaling bottlenecks the making of digital quantum computers, posing challenges from both the quantum and the classical components. We present a classical architecture to cope with a comprehensive list of the latter challenges {\em all at once}, and implement it fully in an end-to-end system by integrating a multi-core RISC-V CPU with our in-house control electronics. Our architecture enables scalable, high-precision control of large quantum processors and accommodates evolving requirements of quantum hardware. A central feature is a microarchitecture executing quantum operations in parallel on arbitrary predefined qubit groups. Another key feature is a reconfigurable quantum instruction set that supports easy qubit re-grouping and instructions extensions. As a demonstration, we implement the widely-studied surface code quantum computing workflow, which is instructive for being demanding on both the controllers and the integrated classical computation. Our design, for the first time, reduces instruction issuing and transmission costs to constants, which do not scale with the number of qubits, without adding any overheads in decoding or dispatching. Rather than relying on specialized hardware for syndrome decoding, our system uses a dedicated multi-core CPU for both qubit control and classical computation, including syndrome decoding. This simplifies the system design and facilitates load-balancing between the quantum and classical components. We implement recent proposals as decoding firmware on a RISC-V system-on-chip (SoC) that parallelizes general inner decoders. By using our in-house Union-Find and PyMatching 2 implementations, we can achieve unprecedented decoding capabilities of up to distances 47 and 67 with the currently available SoCs, under realistic and optimistic assumptions of physical error rate $p=0.001 and p=0.0001, respectively, all in just 1 \textmu s.

1.The Mollow triplets under few-photon excitation

Authors:Bang Wu, Xu-Jie Wang, Li Liu, Guoqi Huang, Wenyan Wang, Hanqing Liu, Haiqiao Ni, Zhichuan Niu, Zhiliang Yuan

Abstract: Resonant excitation is an essential tool in the development of semiconductor quantum dots (QDs) for quantum information processing. One central challenge is to enable a transparent access to the QD signal without post-selection information loss. A viable path is through cavity enhancement, which has successfully lifted the resonantly scattered field strength over the laser background under \emph{weak} excitation. Here, we extend this success to the \emph{saturation} regime using a QD-micropillar device with a Purcell factor of 10.9 and an ultra-low background cavity reflectivity of just 0.0089. We achieve a signal to background ratio of 50 and an overall system responsivity of 3~\%, i.e., we detect on average 0.03 resonantly scattered single photons for every incident laser photon. Raising the excitation to the few-photon level, the QD response is brought into saturation where we observe the Mollow triplets as well as the associated cascade single photon emissions, without resort to any laser background rejection technique. Our work offers a new perspective toward QD cavity interface that is not restricted by the laser background.

2.Accelerating relaxation through Liouvillian exceptional point

Authors:Yan-Li Zhou, Xiao-Die Yu, Chun-Wang Wu, Xie-Qian Li, Jie Zhang, Weibin Li, Ping-Xing Chen

Abstract: We investigate speeding up of relaxation of Markovian open quantum systems with the Liouvillian exceptional point (LEP), where the slowest decay mode degenerate with a faster decay mode. The degeneracy significantly increases the gap of the Liouvillian operator, which determines the timescale of such systems in converging to stationarity, and hence accelerates the relaxation process. We explore an experimentally relevant three level atomic system, whose eigenmatrices and eigenspectra are obtained completely analytically. This allows us to gain insights in the LEP and examine respective dynamics with details. We illustrate that the gap can be further widened through Floquet engineering, which further accelerates the relaxation process. Finally, we extend this approach to analyze laser cooling of trapped ions, where vibrations (phonons) couple to the electronic states. An optimal cooling condition is obtained analytically, which agrees with both existing experiments and numerical simulations. Our study provides analytical insights in understanding LEP, as well as in controlling and optimizing dissipative dynamics of atoms and trapped ions.

3.Constructions of $k$-uniform states in heterogeneous systems

Authors:Keqin Feng, Lingfei Jin, Chaoping Xing, Chen Yuan

Abstract: A pure quantum state of $n$ parties associated with the Hilbert space $\CC^{d_1}\otimes \CC^{d_2}\otimes\cdots\otimes \CC^{d_n}$ is called $k$-uniform if all the reductions to $k$-parties are maximally mixed. The $n$ partite system is called homogenous if the local dimension $d_1=d_2=\cdots=d_n$, while it is called heterogeneous if the local dimension are not all equal. $k$-uniform sates play an important role in quantum information theory. There are many progress in characterizing and constructing $k$-uniform states in homogeneous systems. However, the study of entanglement for heterogeneous systems is much more challenging than that for the homogeneous case. There are very few results known for the $k$-uniform states in heterogeneous systems for $k>3$. We present two general methods to construct $k$-uniform states in the heterogeneous systems for general $k$. The first construction is derived from the error correcting codes by establishing a connection between irredundant mixed orthogonal arrays and error correcting codes. We can produce many new $k$-uniform states such that the local dimension of each subsystem can be a prime power. The second construction is derived from a matrix $H$ meeting the condition that $H_{A\times \bar{A}}+H^T_{\bar{A}\times A}$ has full rank for any row index set $A$ of size $k$. These matrix construction can provide more flexible choices for the local dimensions, i.e., the local dimensions can be any integer (not necessarily prime power) subject to some constraints. Our constructions imply that for any positive integer $k$, one can construct $k$-uniform states of a heterogeneous system in many different Hilbert spaces.

4.How to wire a 1000-qubit trapped ion quantum computer

Authors:M. Malinowski, D. T. C. Allcock, C. J. Ballance

Abstract: One of the most formidable challenges of scaling up quantum computers is that of control signal delivery. Today's small-scale quantum computers typically connect each qubit to one or more separate external signal sources. This approach is not scalable due to the I/O limitations of the qubit chip, necessitating the integration of control electronics. However, it is no small feat to shrink control electronics into a small package that is compatible with qubit chip fabrication and operation constraints without sacrificing performance. This so-called "wiring challenge" is likely to impact the development of more powerful quantum computers even in the near term. In this paper, we address the wiring challenge of trapped-ion quantum computers. We describe a control architecture called WISE (Wiring using Integrated Switching Electronics), which significantly reduces the I/O requirements of ion trap quantum computing chips without compromising performance. Our method relies on judiciously integrating simple switching electronics into the ion trap chip - in a way that is compatible with its fabrication and operation constraints - while complex electronics remain external. To demonstrate its power, we describe how the WISE architecture can be used to operate a fully connected 1000-qubit trapped ion quantum computer using ~ 200 signal sources at a speed of ~ 40 - 2600 quantum gate layers per second.

5.Quantum Text Classifier -- A Synchronistic Approach Towards Classical and Quantum Machine Learning

Authors:Dr. Prabhat Santi, Kamakhya Mishra, Sibabrata Mohanty

Abstract: Although it will be a while before a practical quantum computer is available, there is no need to hold off. Methods and algorithms are being developed to demonstrate the feasibility of running machine learning (ML) pipelines in QC (Quantum Computing). There is a lot of ongoing work on general QML (Quantum Machine Learning) algorithms and applications. However, a working model or pipeline for a text classifier using quantum algorithms isn't available. This paper introduces quantum machine learning w.r.t text classification to readers of classical machine learning. It begins with a brief description of quantum computing and basic quantum algorithms, with an emphasis on building text classification pipelines. A new approach is introduced to implement an end-to-end text classification framework (Quantum Text Classifier - QTC), where pre- and post-processing of data is performed on a classical computer, and text classification is performed using the QML algorithm. This paper also presents an implementation of the QTC framework and available quantum ML algorithms for text classification using the IBM Qiskit library and IBM backends.

6.Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics

Authors:Xiaodong Zhang, Weihua Zhang, Jiongning Che, Barbara Dietz

Abstract: We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T ) invariance and chaotic classical counterpart. High-precision experiments are performed with a flat superconducting microwave resonator with circular shape in which T invariance and a chaotic dynamics are induced by magnetizing a ferrite disk placed at its center. We determine a complete sequence of ' 1000 eigenfrequencies and verify analytical predictions for the spectral properties of the Rosenzweig-Porter (RP) model which, currently, is under intensive study in the context of many-body quantum chaos as it exhibits ergodic, fractal and localized phases. Furthermore, we introduce based on this RP model and the Heidelberg approach a random-matrix model for the scattering (S) matrix of the corresponding open quantum system and show that it perfectly reproduces the fluctuation properties of the measured S matrix of the microwave resonator.

7.A sequentially generated variational quantum circuit with polynomial complexity

Authors:Xiaokai Hou, Qingyu Li, Man-Hong Yung, Xusheng Xu, Zizhu Wang, Chu Guo, Xiaoting Wang

Abstract: Variational quantum algorithms have been a promising candidate to utilize near-term quantum devices to solve real-world problems. The powerfulness of variational quantum algorithms is ultimately determined by the expressiveness of the underlying quantum circuit ansatz for a given problem. In this work, we propose a sequentially generated circuit ansatz, which naturally adapts to 1D, 2D, 3D quantum many-body problems. Specifically, in 1D our ansatz can efficiently generate any matrix product states with a fixed bond dimension, while in 2D our ansatz generates the string-bond states. As applications, we demonstrate that our ansatz can be used to accurately reconstruct unknown pure and mixed quantum states which can be represented as matrix product states, and that our ansatz is more efficient compared to several alternatives in finding the ground states of some prototypical quantum many-body systems as well as quantum chemistry systems, in terms of the number of quantum gate operations.

8.London quantum-secured metro network

Authors:Andrew Lord, Robert Woodward, Shinya Murai, Hideaki Sato, James Dynes, Paul Wright, Catherine White, Russell Davey, Mark Wilkinson, Piers Clinton-Tarestad, Ian Hawkins, Kristopher Farrington, Andrew Shields

Abstract: We describe a London Quantum-Secured Metro Network using Quantum Key Distribution between three London nodes together with customer access tails. The commercially- eady solution is fully integrated into the BT network and on-boarded its first customer.

9.Software-defined quantum network using a QKD-secured SDN controller and encrypted messages

Authors:R. S. Tessinari, R. I. Woodward, A. J. Shields

Abstract: We propose and implement a software-defined network architecture that integrates the QKD SDN Controller within the QKD node, enabling it to use quantum keys to secure its communication with SDN agents while optimizing QKD-keys consumption.

10.Unconditionally secure quantum bit commitment using modified double-slit and unstable particles

Authors:Chi-Yee Cheung

Abstract: We note that the proof of the no-go theorem of unconditionally secure quantum bit commitment is based on a model which is not universal. For protocols not described by the model, this theorem does not apply. Using unstable particles and a modified double-slit setup, we construct such a protocol and show that it is unconditionally secure. In this protocol, the committer transfers no quantum states to the receiver.

11.Quantum state smoothing cannot be assumed classical even when the filtering and retrofiltering are classical

Authors:Kiarn T. Laverick, Prahlad Warszawski, Areeya Chantasri, Howard M. Wiseman

Abstract: State smoothing is a technique to estimate a state at a particular time, conditioned on information obtained both before (past) and after (future) that time. For a classical system, the smoothed state is a normalized product of the $\textit{filtered state}$ (a state conditioned only on the past measurement information and the initial preparation) and the $\textit{retrofiltered effect}$ (depending only on the future measurement information). For the quantum case, whilst there are well-established analogues of the filtered state ($\rho_{\rm F}$) and retrofiltered effect ($\hat E_{\rm R}$), their product does not, in general, provide a valid quantum state for smoothing. However, this procedure does seem to work when $\rho_{\rm F}$ and $\hat E_{\rm R}$ are mutually diagonalizable. This fact has been used to obtain smoothed quantum states -- more pure than the filtered states -- in a number of experiments on continuously monitored quantum systems, in cavity QED and atomic systems. In this paper we show that there is an implicit assumption underlying this technique: that if all the information were known to the observer, the true system state would be one of the diagonal basis states. This assumption does not necessarily hold, as the missing information is quantum information. It could be known to the observer only if it were turned into a classical measurement record, but then its nature depends on the choice of measurement. We show by a simple model that, depending on that measurement choice, the smoothed quantum state can: agree with that from the classical method; disagree with it but still be co-diagonal with it; or not even be co-diagonal with it. That is, just because filtering and retrofiltering appear classical does not mean classical smoothing theory is applicable in quantum experiments.

12.Statistical link between Bell nonlocality and uncertainty relations

Authors:Li-Yi Hsu

Abstract: Bell nonlocality and uncertainty relations are distinct features of quantum theory from classical physics. Bell nonlocality concerns the correlation strength among local observables on different quantum particles, whereas the uncertainty relations set the lower bound of the sum or product of the variance square of observables. Here we establish the statistical link between these two quantum characters using the Aharonov-Vaidman identity. Therein, the upper bounds of Bell-type inequalities are expressed in terms of the product of the local sum of the variance square. On the other hand, instead of evaluating local uncertainty relations, the uncertainty relations on two or more quantum systems are upper-bounded by the amount of Bell nonlocality therein.

13.Interplay between finite thickness and chirality effects on the Casimir-Lifshitz torque with nematic cholesteric liquid crystals

Authors:Wijnand Broer, Rudolf Podgornik

Abstract: We theoretically investigate the combined effects of the chirality and the finite total thickness of nematic cholesteric liquid crystals on the Casimir-Lifshitz torque. We find that, the larger the thickness, the more sinusoidal the angular dependence of the torque becomes. We use a Fourier decomposition to quantify this result. The general direction of the torque depends on whether the configuration of two cholesterics is heterochiral or homochiral.

14.Free Space Continuous Variable Quantum Key Distribution with Discrete Phases

Authors:Anju Rani, Pooja Chandravanshi, Jayanth Ramakrishnan, Pravin Vaity, P. Madhusudhan, Tanya Sharma, Pranav Bhardwaj, Ayan Biswas, R. P. Singh

Abstract: Quantum Key Distribution (QKD) offers unconditional security in principle. Many QKD protocols have been proposed and demonstrated to ensure secure communication between two authenticated users. Continuous variable (CV) QKD offers many advantages over discrete variable (DV) QKD since it is cost-effective, compatible with current classical communication technologies, efficient even in daylight, and gives a higher secure key rate. Keeping this in view, we demonstrate a discrete modulated CVQKD protocol in the free space which is robust against polarization drift. We also present the simulation results with a noise model to account for the channel noise and the effects of various parameter changes on the secure key rate. These simulation results help us to verify the experimental values obtained for the implemented CVQKD.

15.A Lindblad master equation capable of describing hybrid quantum systems in the ultra-strong coupling regime

Authors:Maksim Lednev, Francisco J. García-Vidal, Johannes Feist

Abstract: Despite significant theoretical efforts devoted to studying the interaction between quantized light modes and matter, the so-called ultra-strong coupling regime still presents significant challenges for theoretical treatments and prevents the use of many common approximations. Here we demonstrate an approach that can describe the dynamics of hybrid quantum systems in any regime of interaction for an arbitrary electromagnetic (EM) environment. We extend a previous method developed for few-mode quantization of arbitrary systems to the case of ultrastrong light-matter coupling, and show that even such systems can be treated using a Lindblad master equation where decay operators act only on the photonic modes by ensuring that the effective spectral density of the EM environment is sufficiently suppressed at negative frequencies. We demonstrate the validity of our framework and show that it outperforms current state-of-the-art master equations for a simple model system, and then study a realistic nanoplasmonic setup where existing approaches cannot be applied.

16.Clifford group is not a semidirect product in dimensions $N$ divisible by four

Authors:Miroslav Korbelář, Jiří Tolar

Abstract: The paper is devoted to projective Clifford groups of quantum $N$-dimensional systems. Clearly, Clifford gates allow only the simplest quantum computations which can be simulated on a classical computer (Gottesmann-Knill theorem). However, it may serve as a cornerstone of full quantum computation. As to its group structure it is well-known that -- in $N$-dimensional quantum mechanics -- the Clifford group is a natural semidirect product provided the dimension $N$ is an odd number. For even $N$ special results on the Clifford groups are scattered in the mathematical literature, but they don't concern the semidirect structure. Using appropriate group presentation of $SL(2,Z_N)$ it is proved that for even $N$ projective Clifford groups are not natural semidirect products if and only if $N$ is divisible by four.

17.Protocol for suppression of noise from stimulated multi-photon emissions in concatenated entanglement swapping links and quantum repeaters

Authors:Yousef K. Chahine, Ian R. Nemitz, John D. Lekki

Abstract: Multi-photon emissions constitute a fundamental source of noise in quantum repeaters and other quantum communication protocols when probabilistic photon sources are employed. In this paper, it is shown that by alternating the Bell state measurement (BSM) basis in concatenated entanglement swapping links one can automatically identify and discard many errors from stimulated multi-photon emissions. The proposed protocol is shown to completely eliminate the dominant quadratic growth of multi-photon errors with the length of the repeater chain. Furthermore, it is shown that the protocol can be employed in satellite-assisted entanglement distribution links to enable links which are more robust in the presence of imbalanced channel losses. The analysis introduces a convenient calculus based on Clifford algebra for modeling concatenated entanglement swapping links with multi-photon emissions. In particular, we present a compact expression for the fidelity of the Bell state produced by a repeater chain of arbitrary length including noise from double-pair emissions.

18.Robust excitation of C-band quantum dots for enhanced quantum communication

Authors:Michal Vyvlecka University of Vienna, Faculty of Physics & Vienna Doctoral School in Physics & Vienna Center for Quantum Science and Technology, Boltzmanngasse 5, A-1090 Vienna, Austria, Lennart Jehle University of Vienna, Faculty of Physics & Vienna Doctoral School in Physics & Vienna Center for Quantum Science and Technology, Boltzmanngasse 5, A-1090 Vienna, Austria, Cornelius Nawrath Institut für Halbleiteroptik und Funktionelle Grenzflächen, Center for Integrated Quantum Science and Technology, Francesco Giorgino University of Vienna, Faculty of Physics & Vienna Doctoral School in Physics & Vienna Center for Quantum Science and Technology, Boltzmanngasse 5, A-1090 Vienna, Austria, Mathieu Bozzio Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Vienna, Austria, Robert Sittig Institut für Halbleiteroptik und Funktionelle Grenzflächen, Center for Integrated Quantum Science and Technology, Michael Jetter Institut für Halbleiteroptik und Funktionelle Grenzflächen, Center for Integrated Quantum Science and Technology, Simone L. Portalupi Institut für Halbleiteroptik und Funktionelle Grenzflächen, Center for Integrated Quantum Science and Technology, Peter Michler Institut für Halbleiteroptik und Funktionelle Grenzflächen, Center for Integrated Quantum Science and Technology, Philip Walther Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Vienna, Austria Christian Doppler Laboratory for Photonic Quantum Computer, Faculty of Physics, University of Vienna, Vienna, Austria

Abstract: Building a quantum internet requires efficient and reliable quantum hardware, from photonic sources to quantum repeaters and detectors, ideally operating at telecommunication wavelengths. Thanks to their high brightness and single-photon purity, quantum dot (QD) sources hold the promise to achieve high communication rates for quantum-secured network applications. Furthermore, it was recently shown that excitation schemes, such as longitudinal acoustic phonon-assisted (LA) pumping, provide security benefits by scrambling the coherence between the emitted photon-number states. In this work, we investigate further advantages of LA-pumped quantum dots with emission in the telecom C-band as a core hardware component of the quantum internet. We experimentally demonstrate how varying the pump energy and spectral detuning with respect to the excitonic transition can improve quantum-secured communication rates and provide stable emission statistics regardless of network-environment fluctuations. These findings have significant implications for general implementations of QD single-photon sources in practical quantum communication networks.

19.NASA's Cold Atom Laboratory: Four Years of Quantum Science Operations in Space

Authors:Kamal Oudrhiri, James M. Kohel, Nate Harvey, James R. Kellogg, David C. Aveline, Roy L. Butler, Javier Bosch-Lluis, John L. Callas, Leo Y. Cheng, Arvid P. Croonquist, Walker L. Dula, Ethan R. Elliott, Jose E. Fernandez, Jorge Gonzales, Raymond J. Higuera, Shahram Javidnia, Sandy M. Kwan, Norman E. Lay, Dennis K. Lee, Irena Li, Gregory J. Miles, Michael T. Pauken, Kelly L. Perry, Leah E. Phillips, Diane C. Malarik, DeVon W. Griffin, Bradley M. Carpenter, Michael P. Robinson, Kirt Costello Sarah K. Rees, Matteo S. Sbroscia, Christian Schneider, Robert F. Shotwell, Gregory Y. Shin, Cao V. Tran, Michel E. William, Jason R. Williams, Oscar Yang, Nan Yu, Robert J. Thompson

Abstract: The Cold Atom Laboratory (CAL) is a quantum facility for studying ultra-cold gases in the microgravity environment of the International Space Station. It enables research in a temperature regime and force-free environment inaccessible to terrestrial laboratories. In the microgravity environment, observation times over a few seconds and temperatures below 100 pK are achievable, unlocking the potential to observe new quantum phenomena. CAL launched to the International Space Station in May 2018 and has been operating since then as the world's first multi-user facility for studying ultra\-cold atoms in space. CAL is the first quantum science facility to produce the fifth state of matter called a Bose-Einstein condensate with rubidium-87 and potassium-41 in Earth orbit. We will give an overview of CAL's operational setup, outline its contributions to date, present planned upgrades for the next few years, and consider design choices for microgravity BEC successor-mission planning.

1.The Vector-Model Wavefunction: spatial description and wavepacket formation of quantum-mechanical angular momenta

Authors:T. Peter Rakitzis, Michail E. Koutrakis, George E. Katsoprinakis

Abstract: In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta (\theta - \theta_m) ~e^{i(j+1/2)\chi}$, which treats $j$ in the $|jm>$ state as a three-dimensional entity, is an asymptotic eigenfunction of angular-momentum operators; $\phi$, $\theta$, $\chi$ are the Euler angles, and $cos \theta_m=(m/|j|)$ is the Vector-Model polar angle. The $j_m (\phi,\theta,\chi)$ gives a computationally simple description of particle and orbital-angular-momentum wavepackets (constructed from Gaussian distributions in $j$ and $m$) which predicts the effective wavepacket angular uncertainty relations for $\Delta m \Delta \phi $, $\Delta j \Delta \chi$, and $\Delta\phi\Delta\theta$, and the position of the particle-wavepacket angular motion on the orbital plane. The particle-wavepacket rotation can be experimentally probed through continuous and non-destructive $j$-rotation measurements. We also use the $j_m (\phi,\theta,\chi)$ to determine well-known asymptotic expressions for Clebsch-Gordan coefficients, Wigner d-functions, the gyromagnetic ratio of elementary particles, $g=2$, and the m-state-correlation matrix elements, $<j_3 m_3|j_{1X} j_{2X}|j_3 m_3>$. Interestingly, for low j, even down to $j=1/2$, these expressions are either exact (the last two) or excellent approximations (the first two), showing that $j_m (\phi,\theta,\chi)$ gives a useful spatial description of quantum-mechanical angular momentum, and provides a smooth connection with classical angular momentum.

2.Optimization of Tensor Network Codes with Reinforcement Learning

Authors:Caroline Mauron, Terry Farrelly, Thomas M. Stace

Abstract: Tensor network codes enable structured construction and manipulation of stabilizer codes out of small seed codes. Here, we apply reinforcement learning to tensor network code geometries and demonstrate how optimal stabilizer codes can be found. Using the projective simulation framework, our reinforcement learning agent consistently finds the best possible codes given an environment and set of allowed actions, including for codes with more than one logical qubit. The agent also consistently outperforms a random search, for example finding an optimal code with a $10\%$ frequency after 1000 trials, vs a theoretical $0.16\%$ from random search, an improvement by a factor of 65.

3.Concrete Quantum Channels and Algebraic Structure of Abstract Quantum Channels

Authors:M. N. N. Namboodiri

Abstract: Construction and testing of preconditioners of Toeplitz/block Toeplitz matrices using Korovkin's classic theorems of positive linear approximations are known. Later the map implementing preconditioners was observed to be a completely positive map, and this structure led to an abstract formulation of Korovkin-type theorems in a non-commutative setting. Interestingly enough, these preconditioner maps' properties satisfy the properties of an abstract quantum channel in quantum information theory. In this short article, this viewpoint is discussed by computing related quantities such as Kraus representation, channel capacity, fidelity etc. Moreover, the algebraic properties of the class of quantum channels are also discussed.

4.Entanglement generation and detection in split exciton-polariton condensates

Authors:Jingyan Feng, Hui Li, Zheng Sun, Tim Byrnes

Abstract: We propose a method of generating and detecting entanglement in two spatially separated excitonpolariton Bose-Einstein condensates (BECs) at steady-state. In our scheme we first create a spinor polariton BEC, such that steady-state squeezing is obtained under a one-axis twisting interaction. Then the condensate is split either physically or virtually, which results in entanglement generated between the two parts. A virtual split means that the condensate is not physically split, but its near-field image is divided into two parts and the spin correlations are deduced from polarization measurements in each half. We theoretically model and examine logarithmic negativity criterion and several correlation-based criteria to show that entanglement exists under experimentally achievable parameters.

5.Wall-Collision Effect on Optically-Polarized Atoms in Small and Hot Vapor Cells

Authors:Yue Chang, Jie Qin

Abstract: In atomic vapor cells, atoms collide with the inner surface, causing their spin to randomize on the walls. This wall-depolarizing effect is diffusive, and it becomes more pronounced in smaller vapor cells under high temperatures. In this work, we investigate the polarization of optically-pumped alkali-metal atoms in a millimeter-sized cell heated to $% 150 $ Celsius. We consider two extreme boundary conditions: fully depolarizing and nondepolarizing boundaries, and we provide an analytical estimation of the polarization difference between them. In the nondepolarizing case, the pump beam's absorption is proportional to the average atomic polarization. However, for fully depolarizing walls, the absorption peak may correspond to a polarization minimum. To mitigate the wall effect, we propose reducing the pump beam's diameter while maintaining the pump power to prevent illumination of the cell wall and increase the pump intensity in the central area. This is crucial for compact vapor-cell devices where the laser frequency can not be detuned since it is locked to the absorption peaks. Additionally, we analyze the wall-depolarizing effect on the performance of an alkali-metal atomic magnetometer operating in the spin-exchange relaxation-free regime. We show that the signal strength is highly limited by wall collisions, and we provide an upper bound for it.

6.Quantum sensing for particle physics

Authors:Steven D. Bass, Michael Doser

Abstract: Quantum sensing is a rapidly growing approach to probe fundamental physics, pushing the frontiers with precision measurements in our quest to understand the deep structure of matter and its interactions. This field uses properties of quantum mechanics in the detectors to go beyond traditional measurement techniques. Key particle physics topics where quantum sensing can play a vital role include neutrino properties, tests of fundamental symmetries (Lorentz invariance and the equivalence principle including searches for possible variations in fundamental constants as well as searches for electric dipole moments), the search for dark matter and testing ideas about the nature of dark energy. Interesting new sensor technologies include atom interferometry, optomechanical devices, and atomic and nuclear clocks including with entanglement.This Perspective explores the opportunities for these technologies in future particle physics experiments, opening new windows on the structure of the Universe.

7.Generalized quantum geometric tensor for excited states using the path integral approach

Authors:Sergio B. Juárez, Diego Gonzalez, Daniel Gutiérrez-Ruiz, J. David Vergara

Abstract: The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states, making it useful to characterize excited state quantum phase transitions (ESQPT). In this setting, we also generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates. This gives rise to an alternative approach to the quantum covariance matrix, from which we can get information about the quantum entanglement of Gaussian states through tools such as purity and von Neumann entropy. Second, we demonstrate the equivalence between the formulation of the quantum geometric tensor in the path integral formalism and other existing methods. Furthermore, we explore the geometric properties of the generalized quantum metric tensor in depth by calculating the Ricci tensor and scalar curvature for several quantum systems, providing insight into this geometric information.

8.Amplitude and phase noise in Two-membrane cavity optomechanics

Authors:Francesco Marzioni, Francesco Rasponi, Paolo Piergentili, Riccardo Natali, Giovanni Di Giuseppe, David Vitali

Abstract: Cavity optomechanics is a suitable field to explore quantum effects on macroscopic objects, and to develop quantum technologies applications. A perfect control on the laser noises is required to operate the system in such extreme conditions, necessary to reach the quantum regime. In this paper we consider a Fabry-Perot cavity, driven by two laser fields, with two partially reflective SiN membranes inside it. We describe the effects of amplitude and phase noise on the laser introducing two additional noise terms in the Langevin equations of the system's dynamics. Experimentally, we add an artificial source of noise on the laser. We calibrate the intensity of the noise we inject into the system, and we check the validity of the theoretical model. This procedure provides an accurate description of the effects of a noisy laser in the optomechanical setup, and it allows to quantify the amount of noise.

9.Fermionic matter-wave quantum optics with cold-atom impurity models

Authors:Bennet Windt, Miguel Bello, Eugene Demler, J. Ignacio Cirac

Abstract: Motivated by recent cold-atom realisations of matter-wave waveguide QED, we study simple fermionic impurity models and discuss fermionic analogues of several paradigmatic phenomena in quantum optics, including formation of non-trivial bound states, (matter-wave) emission dynamics, and collective dissipation. For a single impurity, we highlight interesting ground-state features, focusing in particular on real-space signatures of an emergent length scale associated with an impurity screening cloud. We also present novel non-Markovian many-body effects in the quench dynamics of single- and multiple-impurity systems, including fractional decay around the Fermi level and multi-excitation population trapping due to bound states in the continuum.

10.Quantum transduction of superconducting qubit in electro-optomechanical and electro-optomagnonical system

Authors:Roson Nongthombam, Pooja Kumari Gupta, Amarendra K. Sarma

Abstract: We study the quantum transduction of a superconducting qubit to an optical photon in electro-optomechanical and electro-optomagnonical systems. The electro-optomechanical system comprises a flux-tunable transmon qubit coupled to a suspended mechanical beam, which then couples to an optical cavity. Similarly, in an electro-optomagnonical system, a flux-tunable transmon qubit is coupled to an optical whispering gallery mode via a magnon excitation in a YIG ferromagnetic sphere. In both systems, the transduction process is done in sequence. In the first sequence, the qubit states are encoded in coherent excitations of phonon/magnon modes through the phonon/magnon-qubit interaction, which is non-demolition in the qubit part. We then measure the phonon/magnon excitations, which reveal the qubit states, by counting the average number of photons in the optical cavities. The measurement of the phonon/magnon excitations can be performed at a regular intervals of time.

11.Equivalent noise properties of scalable continuous-variable cluster states

Authors:Blayney W. Walshe, Rafael N. Alexander, Takaya Matsuura, Ben Q. Baragiola, Nicolas C. Menicucci

Abstract: Optical continuous-variable cluster states (CVCSs) in combination with Gottesman-Kitaev-Preskill~(GKP) qubits enable fault-tolerant quantum computation so long as these resources are of high enough quality. Previous studies concluded that a particular CVCS, the quad rail lattice~(QRL), exhibits lower GKP gate-error rate than others do. We show in this work that many other experimentally accessible CVCSs also achieve this level of performance by identifying operational equivalences to the QRL. Under this equivalence, the GKP Clifford gate set for each CVCS maps straightforwardly from that of the QRL, inheriting its noise properties. Furthermore, each cluster state has at its heart a balanced four-splitter -- the four-mode extension to a balanced beam splitter. We classify all four-splitters, show they form a single equivalence class under SWAP and parity operators, and we give a construction of any four-splitter with linear optics, thus extending the toolbox for theoretical and experimental cluster-state design and analysis.

12.Quantum channel decomposition with pre- and post-selection

Authors:Ryo Nagai, Shu Kanno, Yuki Sato, Naoki Yamamoto

Abstract: The quantum channel decomposition techniques, which contain the so-called probabilistic error cancellation and gate/wire cutting, are powerful approach for simulating a hard-to-implement (or an ideal) unitary operation by concurrently executing relatively easy-to-implement (or noisy) quantum channels. However, such virtual simulation necessitates an exponentially large number of decompositions, thereby significantly limiting their practical applicability. This paper proposes a channel decomposition method for target unitaries that have their input and output conditioned on specific quantum states, namely unitaries with pre- and post-selection. Specifically, we explicitly determine the requisite number of decomposing channels, which could be significantly smaller than the selection-free scenario. Furthermore, we elucidate the structure of the resulting decomposed unitary. We demonstrate an application of this approach to the quantum linear solver algorithm, highlighting the efficacy of the proposed method.

13.Waveguide QED with Mössbauer Nuclei

Authors:Petar Andrejić, Leon Merten Lohse, Adriana Pálffy

Abstract: Thin-film nanostructures with embedded M\"ossbauer nuclei have been successfully used for x-ray quantum optical applications with hard x-rays coupling in grazing incidence. Here we address theoretically a new geometry, in which hard x-rays are coupled in forward incidence (front coupling), setting the stage for waveguide QED with nuclear x-ray resonances. We develop a general model based on the Green's function formalism of the field-nucleus interaction in one dimensional waveguides, and show that it combines aspects of both nuclear forward scattering, visible as dynamical beating in the spatio-temporal response, and the resonance structure from grazing incidence, visible in the spectrum of guided modes. The interference of multiple modes is shown to play an important role, resulting in beats with wavelengths on the order of tens of microns, on the scale of practical photolithography. This allows for the design of special sample geometries to explore the resonant response or micro-striped waveguides, opening a new toolbox of geometrical design for hard X-ray quantum optics.

14.Petz recovery maps: Geometrical aspects and an analysis for qudit channels

Authors:Lea Lautenbacher, Vinayak Jagadish, Francesco Petruccione, Nadja K. Bernardes

Abstract: Using the Petz map, we investigate the potential of state recovery when exposed to dephasing and amplitude-damping channels. Specifically, we analyze the geometrical aspects of the Petz map for the qubit case, which is linked to the change in the volume of accessible states. Our findings suggest that the geometrical characterization can serve as a potent tool for understanding the details of the recovery procedure. Furthermore, we extend our analysis to qudit channels by devising a state-independent framework that quantifies the ability of the Petz map to recover a state for any dimension. Under certain conditions, the dimensionality plays a role in state recovery.

15.Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

Authors:E. I. Jafarov, S. M. Nagiyev

Abstract: Dynamical symmetry algebra for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. Selecting the starting point as a well-known factorization method of the Hamiltonian under consideration, we have found three basis elements of this algebra. The algebra defined through those basis elements is a $\mathfrak{su}\left(1,1 \right)$ Heisenberg-Lie algebra. Different special cases and the limit relations from the basis elements to the Heisenberg-Weyl algebra of the non-relativistic quantum harmonic oscillator are discussed, too.

16.Single-photon source over the terahertz regime

Authors:Caspar Groiseau, Antonio I. Fernández Domínguez, Diego Martín Cano, Carlos Sánchez Muñoz

Abstract: We present a proposal for a tunable source of single photons operating in the terahertz (THz) regime. This scheme transforms incident visible photons into quantum THz radiation by driving a single polar quantum emitter with an optical laser, with its permanent dipole enabling dressed THz transitions enhanced by the resonant coupling to a cavity. This mechanism offers optical tunability of properties such as the frequency of the emission or its quantum statistics (ranging from antibunching to entangled multi-photon states) by modifying the intensity and frequency of the drive. We show that the implementation of this proposal is feasible with state-of-the-art photonics technology.

17.Universal defects statistics with strong long-range interactions

Authors:Stefano Gherardini, Lorenzo Buffoni, Nicolò Defenu

Abstract: Quasi-static transformations, or slow quenches, of many-body quantum systems across quantum critical points create topological defects. The Kibble-Zurek mechanism regulates the appearance of defects in a local quantum system through a classical combinatorial process. However, long-range interactions disrupt the conventional Kibble-Zurek scaling and lead to a density of defects that is independent of the rate of the transformation. In this study, we analytically determine the complete full counting statistics of defects generated by slow annealing a strong long-range system across its quantum critical point. We demonstrate that the mechanism of defect generation in long-range systems is a purely quantum process with no classical equivalent. Furthermore, universality is not only observed in the defect density but also in all the moments of the distribution. Our findings can be tested on various experimental platforms, including Rydberg gases and trapped ions.

18.Measuring Magic via Multifractal Flatness

Authors:Xhek Turkeshi, Marco Schirò, Piotr Sierant

Abstract: Universal quantum computing requires non-stabilizer (magic) quantum states. Quantifying the nonstabilizerness and relating it to other quantum resources is vital for characterizing the complexity of quantum many-body systems. In this work, we prove that a quantum state is a stabilizer if and only if all states belonging to its Clifford orbit have a flat probability distribution on the computational basis. This implies, in particular, that multifractal states are magic. We introduce multifractal flatness, a measure based on the participation entropy that quantifies the wave function distribution flatness. We demonstrate that this quantity is analytically related to the stabilizer entropy of the state and present several examples elucidating the relationship between multifractality and nonstabilizerness. In particular, we show that the multifractal flatness provides an experimentally and computationally viable nonstabilizerness certification. Our work unravels a direct relation between the nonstabilizerness of a quantum state and its wave function structure.

19.Security of differential phase shifted QKD against explicit individual attacks

Authors:Valliamai Ramanathan, Anil Prabhakar, Prabha Mandayam

Abstract: Quantum key distribution (QKD) is known to be unconditionally secure in principle, but quantifying the security of QKD protocols from a practical standpoint continues to remain an important challenge. Here, we focus on phase-based QKD protocols and characterize the security of the 3 and n-pulse Differential-Phase-Shifted Quantum Key Distribution (DPS QKD) protocols against individual attacks. In particular, we focus on the minimum error discrimination (MED) and cloning attacks and obtain the corresponding bit error rates and the collision probability in the presence of these attacks. We compare the secure key rates thus obtained with the known theoretical lower bounds derived considering a general individual attack. In a departure from the theoretical lower bounds which has no explicit attack strategies, our work provides a practical assessment of the security of these phase-based protocols based on attacks with known implementations.

20.Fast Partitioning of Pauli Strings into Commuting Families for Optimal Expectation Value Measurements of Dense Operators

Authors:Ben Reggio, Nouman Butt, Andrew Lytle, Patrick Draper

Abstract: The Pauli strings appearing in the decomposition of an operator can be can be grouped into commuting families, reducing the number of quantum circuits needed to measure the expectation value of the operator. We detail an algorithm to completely partition the full set of Pauli strings acting on any number of qubits into the minimal number of sets of commuting families, and we provide python code to perform the partitioning. The partitioning method scales linearly with the size of the set of Pauli strings and it naturally provides a fast method of diagonalizing the commuting families with quantum gates. We provide a package that integrates the partitioning into Qiskit, and use this to benchmark the algorithm with dense Hamiltonians, such as those that arise in matrix quantum mechanics models, on IBM hardware. We demonstrate computational speedups close to the theoretical limit of $(2/3)^m$ relative to qubit-wise commuting groupings, for $m=2,\dotsc,6$ qubits.

1.Classical shadows based on locally-entangled measurements

Authors:Matteo Ippoliti

Abstract: We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases, generalizing the random Pauli measurement protocol ($n = 1$). We show that entangled measurements ($n\geq 2$) enable nontrivial and potentially advantageous trade-offs in the sample complexity of learning Pauli expectation values. This is sharply illustrated by shadows based on two-qubit Bell measurements: the scaling of sample complexity with Pauli weight $k$ improves quadratically (from $\sim 3^k$ down to $\sim 3^{k/2}$) for many operators, while others become impossible to learn. Tuning the amount of entanglement in the measurement bases defines a family of protocols that interpolate between Pauli and Bell shadows, retaining some of the benefits of both. For large $n$, we show that randomized measurements in $n$-qubit GHZ bases further improve the best scaling to $\sim (3/2)^k$, albeit on an increasingly restricted set of operators. Despite their simplicity and lower hardware requirements, these protocols can match or outperform recently-introduced ``shallow shadows'' in some practically-relevant Pauli estimation tasks.

2.Robust and efficient verification of measurement-based quantum computation

Authors:Zihao Li, Huangjun Zhu, Masahito Hayashi

Abstract: Measurement-based quantum computation is a promising approach for realizing blind and cloud quantum computation. To obtain reliable results in this model, it is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. However, previous verification protocols for this task are too resource consuming or noise susceptible to be applied in practice. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension in the adversarial scenario, which leads to a robust and efficient protocol for verifying blind measurement-based quantum computation. Our protocol requires only local Pauli measurements and is thus easy to realize with current technologies. Nevertheless, it can achieve the optimal scaling behaviors with respect to the system size and the target precision as quantified by the infidelity and significance level, which has never been achieved before. Notably, our protocol can exponentially enhance the scaling behavior with the significance level.

3.Measurement-Device-Independent Quantum Secret Sharing

Authors:Xiao-Qiu Cai, Zi-Fan Liu, Tian-Yin Wang

Abstract: Quantum secret sharing plays an important role in quantum communications and secure multiparty computation. In this paper, we present a new measurement-device-independent quantum secret sharing protocol, which can double the space distance between the dealer and each sharer for quantum transmission compared with prior works. Furthermore, it is experimentally feasible with current technology for requiring just three-particle Greenberger-Horne-Zeilinger states and Bell state measurements.

4.A Variational Approach to Unique Determinedness in Pure-state Tomography

Authors:Chao Zhang, Xuanran Zhu, Bei Zeng

Abstract: In quantum state tomography, particularly with pure states, unique determinedness (UD) holds significant importance. This study presents a new variational approach to examining UD, offering a robust solution to the challenges associated with the construction and validation of UD measurement schemes. We put forward an effective algorithm that minimizes a specially defined loss function, enabling the differentiation between UD and non-UD measurement schemes. This leads to the discovery of numerous optimal pure-state Pauli measurement schemes across a variety of dimensions. Additionally, we discern an alignment between uniquely determined among pure states (UDP) and uniquely determined among all states (UDA) in qubit systems when utilizing Pauli measurements, underscoring its unique characteristics. We further bridge the gap between our loss function and the stability of state recovery, bolstered by a theoretical framework. Our study not only propels the understanding of UD in quantum state tomography forward, but also delivers valuable practical insights for experimental applications, highlighting the need for a balanced approach between mathematical optimality and experimental pragmatism.

5.A privacy-preserving publicly verifiable quantum random number generator

Authors:Tanvirul Islam, Anindya Banerji, Chin Jia Boon, Wang Rui, Ayesha Reezwana, James A. Grieve, Rodrigo Piera, Alexander Ling

Abstract: Verifying the quality of a random number generator involves performing computationally intensive statistical tests on large data sets commonly in the range of gigabytes. Limitations on computing power can restrict an end-user's ability to perform such verification. There are also applications where the user needs to publicly demonstrate that the random bits they are using pass the statistical tests without the bits being revealed. We report the implementation of an entanglement-based protocol that allows a third party to publicly perform statistical tests without compromising the privacy of the random bits.

6.Benchmarking a boson sampler with Hamming nets

Authors:Ilia A. Iakovlev, Oleg M. Sotnikov, Ivan V. Dyakonov, Evgeniy O. Kiktenko, Aleksey K. Fedorov, Stanislav S. Straupe, Vladimir V. Mazurenko

Abstract: Analyzing the properties of complex quantum systems is crucial for further development of quantum devices, yet this task is typically challenging and demanding with respect to required amount of measurements. A special attention to this problem appears within the context of characterizing outcomes of noisy intermediate-scale quantum devices, which produce quantum states with specific properties so that it is expected to be hard to simulate such states using classical resources. In this work, we address the problem of characterization of a boson sampling device, which uses interference of input photons to produce samples of non-trivial probability distributions that at certain condition are hard to obtain classically. For realistic experimental conditions the problem is to probe multi-photon interference with a limited number of the measurement outcomes without collisions and repetitions. By constructing networks on the measurements outcomes, we demonstrate a possibility to discriminate between regimes of indistinguishable and distinguishable bosons by quantifying the structures of the corresponding networks. Based on this we propose a machine-learning-based protocol to benchmark a boson sampler with unknown scattering matrix. Notably, the protocol works in the most challenging regimes of having a very limited number of bitstrings without collisions and repetitions. As we expect, our framework can be directly applied for characterizing boson sampling devices that are currently available in experiments.

7.Long-distance continuous-variable quantum key distribution with feasible physical noiseless linear amplifiers

Authors:Michele N. Notarnicola, Stefano Olivares

Abstract: Noiseless linear amplifiers (NLAs) provide a powerful tool to achieve long-distance continuous-variable quantum key distribution (CV-QKD) in the presence of realistic setups with non unit reconciliation efficiency. We address a NLA-assisted CV-QKD protocol implemented via realistic physical NLAs, namely, quantum scissors (QS) and single-photon catalysis (SPC), and compare their performance with respect to the ideal NLA $g^{\hat{n}}$. We investigate also the robustness of two schemes against inefficient conditional detection, and discuss the two alternative scenarios in which the gain associated with the NLA is either fixed or optimized.

8.Simulation of a Variational Quantum Perceptron using Grover's Algorithm

Authors:Nouhaila Innan, Mohamed Bennai

Abstract: The quantum perceptron, the variational circuit, and the Grover algorithm have been proposed as promising components for quantum machine learning. This paper presents a new quantum perceptron that combines the quantum variational circuit and the Grover algorithm. However, this does not guarantee that this quantum variational perceptron with Grover's algorithm (QVPG) will have any advantage over its quantum variational (QVP) and classical counterparts. Here, we examine the performance of QVP and QVP-G by computing their loss function and analyzing their accuracy on the classification task, then comparing these two quantum models to the classical perceptron (CP). The results show that our two quantum models are more efficient than CP, and our novel suggested model QVP-G outperforms the QVP, demonstrating that the Grover can be applied to the classification task and even makes the model more accurate, besides the unstructured search problems.

9.Preparation of cavity Fock state superpositions by reinforcement learning exploiting measurement back-action

Authors:Arthur Perret, Yves Bérubé-Lauzière

Abstract: Preparation of bosonic and general cavity quantum states usually relies on using open-loop control to reach a desired target state. In this work, a measurement-based feedback approach is used instead, exploiting the non-linearity of weak measurements alongside a coherent drive to prepare these states. The extension of previous work on Lyapunov-based control is shown to fail for this task. This prompts for a different approach, and reinforcement learning (RL) is resorted to here for this purpose. With such an approach, cavity eigenstate superpositions can be prepared with fidelities over 98$\%$ using only the measurements back-action as the non-linearity, while naturally incorporating detection of cavity photon jumps. Two different RL frameworks are analyzed: an off-policy approach recently introduced called truncated quantile critic~(TQC) and the on-policy method commonly used in quantum control, namely proximal policy optimization~(PPO). It is shown that TQC performs better at reaching higher target state fidelity preparation.

10.Noise-adapted recovery circuits for quantum error correction

Authors:Debjyoti Biswas, Gaurav M. Vaidya, Prabha Mandayam

Abstract: Implementing quantum error correction (QEC) protocols is a challenging task in today's era of noisy intermediate-scale quantum devices. We present quantum circuits for a universal, noise-adapted recovery map, often referred to as the Petz map, which is known to achieve close-to-optimal fidelity for arbitrary codes and noise channels. While two of our circuit constructions draw upon algebraic techniques such as isometric extension and block encoding, the third approach breaks down the recovery map into a sequence of two-outcome POVMs. In each of the three cases we improve upon the resource requirements that currently exist in the literature. Apart from Petz recovery circuits, we also present circuits that can directly estimate the fidelity between the encoded state and the recovered state. As a concrete example of our circuit constructions, we implement Petz recovery circuits corresponding to the $4$-qubit QEC code tailored to protect against amplitude-damping noise. The efficacy of our noise-adapted recovery circuits is then demonstrated through ideal and noisy simulations on the IBM quantum processors.

11.A quantum XOR oblivious transfer protocol compatible with classical partially homomorphic encryption

Authors:Li Yu, Jie Xu, Fuqun Wang, Chui-Ping Yang

Abstract: XOR oblivious transfer (XOT) is a classical cryptographic primitive which is apparently weaker than 1-out-of-2 oblivious transfer, yet still universal for secure two-party computation. In ideal XOT, Bob initially has two bits, and Alice may choose to obtain either the first bit of Bob's, or the second bit, or their exclusive-or, but does not obtain any more information, while Bob does not learn anything about her choice. In this work we present a quantum protocol which implements the functionality of XOT on classical inputs, with complete security for Alice's input, but only partial security for Bob's input. On the hybrid security front, the protocol can be easily combined with a classical XOR homomorphic encryption scheme to save quantum costs when evaluating linear functions.

12.Thermal light in confined dimensions for "laser" cooling with unfiltered sunlight

Authors:Amanda Younes, Wesley C. Campbell

Abstract: Cooling of systems to sub-kelvin temperatures is usually done using either a cold bath of particles or spontaneous photon scattering from a laser field; in either case, cooling is driven by interaction with a well-ordered, cold (i.e. low entropy) system. However, there have recently been several schemes proposed for ``cooling by heating,'' in which raising the temperature of some mode drives the cooling of the desired system faster. We discuss how to cool a trapped ion to its motional ground state using unfiltered sunlight at $5800\,\mathrm{K}$ to drive the cooling. We show how to treat the statistics of thermal light in a single-mode fiber for delivery to the ion, and show experimentally how the black-body spectrum is strongly modified by being embedded in quasi-one-dimension. Quantitative estimates for the achievable cooling rate with our measured fiber-coupled, low-dimensional sunlight show promise for demonstrating this implementation of cooling by heating.

13.Grover Speedup from Many Forms of the Zeno Effect

Authors:Jesse Berwald, Nick Chancellor, Raouf Dridi

Abstract: It has previously been established that adiabatic quantum computation, operating based on a continuous Zeno effect due to dynamical phases between eigenstates, is able to realise an optimal Grover-like quantum speedup. In other words is able to solve an unstructured search problem with the same $\sqrt{N}$ scaling as Grover's original algorithm. A natural question is whether other manifestations of the Zeno effect can also support an optimal speedup in a physically realistic model (through direct analog application rather than indirectly by supporting a universal gateset). In this paper we show that they can support such a speedup, whether due to measurement, decoherence, or even decay of the excited state into a computationally useless state. Our results also suggest a wide variety of methods to realise speedup which do not rely on Zeno behaviour. We group these algorithms into three families to facilitate a structured understanding of how speedups can be obtained: one based on phase kicks, containing adiabatic computation and continuous-time quantum walks; one based on dephasing and measurement; and finally one based on destruction of the amplitude within the excited state, for which we are not aware of any previous results. These results suggest that there may be exciting opportunities for new paradigms of analog quantum computing based on these effects.

14.Programmable multi-photon quantum interference in a single spatial mode

Authors:Lorenzo Carosini, Virginia Oddi, Francesco Giorgino, Lena M. Hansen, Benoit Seron, Simone Piacentini, Tobias Guggemos, Iris Agresti, Juan Carlos Loredo, Philip Walther

Abstract: The interference of non-classical states of light enables quantum-enhanced applications reaching from metrology to computation. Most commonly, the polarisation or spatial location of single photons are used as addressable degrees-of-freedom for turning these applications into praxis. However, the scale-up for the processing of a large number of photons of such architectures is very resource demanding due to the rapidily increasing number of components, such as optical elements, photon sources and detectors. Here we demonstrate a resource-efficient architecture for multi-photon processing based on time-bin encoding in a single spatial mode. We employ an efficient quantum dot single-photon source, and a fast programmable time-bin interferometer, to observe the interference of up to 8 photons in 16 modes, all recorded only with one detector--thus considerably reducing the physical overhead previously needed for achieving equivalent tasks. Our results can form the basis for a future universal photonics quantum processor operating in a single spatial mode.

1.Deep quantum neural networks form Gaussian processes

Authors:Diego García-Martín, Martin Larocca, M. Cerezo

Abstract: It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of large number of neurons per hidden layer. In this work we prove an analogous result for Quantum Neural Networks (QNNs). Namely, we show that the outputs of certain models based on Haar random unitary or orthogonal deep QNNs converge to Gaussian processes in the limit of large Hilbert space dimension $d$. The derivation of this result is more nuanced than in the classical case due the role played by the input states, the measurement observable, and the fact that the entries of unitary matrices are not independent. An important consequence of our analysis is that the ensuing Gaussian processes cannot be used to efficiently predict the outputs of the QNN via Bayesian statistics. Furthermore, our theorems imply that the concentration of measure phenomenon in Haar random QNNs is much worse than previously thought, as we prove that expectation values and gradients concentrate as $\mathcal{O}\left(\frac{1}{e^d \sqrt{d}}\right)$ -- exponentially in the Hilbert space dimension. Finally, we discuss how our results improve our understanding of concentration in $t$-designs.

2.Scattering of one-dimensional quantum droplets by a reflectionless potential well

Authors:Xiaoxiao Hu, Zhiqiang Li, Yu Guo, Yajiang Chen, Xiaobing Luo

Abstract: We investigate, both analytically and numerically, the scattering of one-dimensional quantum droplets by a P\"{o}schl-Teller reflectionless potential well, confirming that there is a sharp transition between full reflection and full transmission at a certain critical incident speed for both small droplets and large flat-top droplets. We observe sharp differences between small quantum droplet scattering and large quantum droplet scattering. The scattering of small quantum droplets is similar to that of solitons, where a spatially symmetric trapped mode is formed at the critical speed, whereas for large quantum droplets a spatially asymmetric trapped mode is formed. Additionally, a nonmonotonous dependence of the critical speed on the atom number is identified$:$ on the small-droplet side, the critical speed increases with the atom number, while in the flat-top regime, the critical speed decreases with increasing the atom number. Strikingly, the scattering excites internal modes below the particle-emission threshold, preventing the quantum droplets from emitting radiation upon interaction with the potential. Analysis of the small-amplitude excitation spectrum shows that as the number of particles increases, it becomes increasingly difficult to emit particles outside the droplet during scattering, while radiation from solitons cannot be completely avoided. Finally, we study the collision of two quantum droplets at the reflectionless potential, revealing the role of the $\pi$-phase difference ``generator'' played by the reflectionless potential.

3.A Coding Theorem for Rate-Limited Quantum-Classical Optimal Transport

Authors:Hafez M. Garmaroudi, S. Sandeep Pradhan, Jun Chen

Abstract: We establish a coding theorem for rate-limited quantum-classical optimal transport systems with limited classical common randomness. This theorem characterizes the rate region of measurement protocols on a product source state for faithful construction of a given destination state while maintaining the source-destination distortion below a prescribed threshold with respect to a general distortion observable. It also provides a solution to the problem of rate-limited optimal transport, which aims to find the optimal cost of transforming a source quantum state to a destination state via an entanglement-breaking channel with a limited communication rate. The coding theorem is further extended to cover Bosonic continuous-variable quantum systems. The analytical evaluation is performed for the case of a qubit measurement system with unlimited common randomness.

4.Have different kinds of photon-pair sources the same indistinguishability in quantum silicon photonics?

Authors:Jong-Moo Lee, Alessio Baldazzi, Matteo Sanna, Stefano Azzini, Joon Tae Ahn, Myung Lae Lee, Young-Ik Sohn, Lorenzo Pavesi

Abstract: In the same silicon photonic integrated circuit, we compare two types of integrated degenerate photon-pair sources (microring resonators or waveguides) by means of Hong-Ou-Mandel (HOM) interference experiments. Two nominally identical microring resonators are coupled to two nominally identical waveguides which form the arms of a Mach-Zehnder interferometer. This is pumped by two lasers at two different wavelengths to generate by spontaneous four-wave mixing degenerate photon pairs. In particular, the microring resonators can be thermally tuned in or out of resonance with the pump wavelengths, thus choosing either the microring resonators or the waveguides as photon-pair sources, respectively. In this way, an on-chip HOM visibility of 94% with microring resonators and 99% with straight waveguides is measured. We compare our experimental results with theoretical simulations of the joint spectral intensity and the purity of the degenerate photon pairs. We verify that the visibility is connected to the sources' indistinguishability, which can be quantified by the overlap between the joint spectral amplitudes (JSA) of the photon pairs generated by the two sources. We estimate a JSA overlap of 98% with waveguides and 89% with microring resonators.

5.$\boldsymbol{α_{>}(ε) = α_{<}(ε)}$ For The Margolus-Levitin Quantum Speed Limit Bound

Authors:H. F. Chau

Abstract: The Margolus-Levitin (ML) bound says that for any time-independent Hamiltonian, the time needed to evolve from one quantum state to another is at least $\pi \alpha(\epsilon) / (2 \langle E-E_0 \rangle)$, where $\langle E-E_0 \rangle$ is the expected energy of the system relative to the ground state of the Hamiltonian and $\alpha(\epsilon)$ is a function of the fidelity $\epsilon$ between the two state. Nonetheless, only a upper bound $\alpha_{>}(\epsilon)$ and lower bound $\alpha_{<}(\epsilon)$ are known to date although they agree up to at least seven significant figures. By giving a new proof of the ML bound, I show that $\alpha_{>}(\epsilon)$ is indeed equal to $\alpha_{<}(\epsilon)$ and explain why this is the case, thereby filling in this longstanding gap. I also point out a numerical stability issue in computing $\alpha_{>}(\epsilon)$ and report a simple way to evaluate it efficiently and accurately.

6.General Continuity Bounds for Quantum Relative Entropies

Authors:Andreas Bluhm, Ángela Capel, Paul Gondolf, Antonio Pérez-Hernández

Abstract: In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we mostly recover known almost optimal bounds, whereas, for the Belavkin-Staszewski relative entropy, our bounds are new. Finally, we use these continuity bounds to derive a new entropic uncertainty relation.

7.Chordal Graphs and Distinguishability of Quantum Product States

Authors:Comfort Mintah, David W. Kribs, Michael Nathanson, Rajesh Pereira

Abstract: We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the key graph structure that drives distinguishability in one-way LOCC, and we derive a one-way LOCC characterization for chordal graphs that establishes a connection with the theory of matrix completions. We also derive minimality conditions on graph parameters that allow for the determination of indistinguishability of states. We present a number of applications and examples built on these results.

8.Quantum theory without the Axiom of choice, and Lefschetz Quantum Physics

Authors:Koen Thas

Abstract: In this conceptual paper, we discuss quantum formalisms which do not use the famous Axiom of Choice. We also consider the fundamental problem which addresses the (in)correctness of having the complex numbers as the base field for Hilbert spaces in the K{\o}benhavn interpretation of quantum theory, and propose a new approach to this problem (based on the Lefschetz principle). Rather than a Theorem--Proof--paper, this paper describes two new research programs on the foundational level, and focuses on fundamental open questions in these programs which come along the way.

9.Six Measurement Problems of Quantum Mechanics

Authors:F. A. Muller

Abstract: The notorious `measurement problem' has been roving around quantum mechanics for nearly a century since its inception, and has given rise to a variety of `interpretations' of quantum mechanics, which are meant to evade it. We argue that no less than six problems need to be distinguished, and that several of them classify as different types of problems. One of them is what traditionally is called `the measurement problem' (here: the Reality Problem of Measurement Outcomes). Another of them has nothing to do with measurements but is a profound metaphysical problem. We also analyse critically Maudlin's (1995) well-known statement of `three measurements problems', and the clash of the views of Brown (1986) and Stein (1997) on one of the six measurement problems, concerning so-called Insolubility Theorems. Finally, we summarise a solution to one measurement problem which has been largely ignored but tacitly if not explicitly acknowledged.

10.Measurement-induced multipartite-entanglement regimes in collective spin systems

Authors:Pablo M. Poggi, Manuel H. Muñoz-Arias

Abstract: We study the competing effects of collective generalized measurements and interaction-induced scrambling in the dynamics of an ensemble of spin-1/2 particles at the level of quantum trajectories. This setup can be considered as analogous to the one leading to measurement-induced transitions in quantum circuits. We show that the interplay between collective unitary dynamics and measurements leads to three regimes of the average Quantum Fisher Information (QFI), which is a witness of multipartite entanglement, as a function of the monitoring strength. While both weak and strong measurements lead to extensive QFI density (i.e., individual quantum trajectories yield states displaying Heisenberg scaling), an intermediate regime of classical-like states emerges for all system sizes where the measurement effectively competes with the scrambling dynamics and precludes the development of quantum correlations, leading to sub-Heisenberg-limited states. We characterize these regimes and the transitions between them using numerical and analytical tools, and discuss the connections between our findings, entanglement phases in monitored many-body systems, and the quantum-to-classical transition.

11.New and improved bounds on the contextuality degree of multi-qubit configurations

Authors:Axel Muller, Metod Saniga, Alain Giorgetti, Henri de Boutray, Frédéric Holweck

Abstract: We present algorithms and a C code to decide quantum contextuality and evaluate the contextuality degree (a way to quantify contextuality) for a variety of point-line geometries located in binary symplectic polar spaces of small rank. With this code we were not only able to recover, in a more efficient way, all the results of a recent paper by de Boutray et al (J. Phys. A: Math. Theor. 55 475301, 2022), but also arrived at a bunch of new noteworthy results. The paper first describes the algorithms and the C code. Then it illustrates its power on a number of subspaces of symplectic polar spaces whose rank ranges from two to seven. The most interesting new results include: (i) non-contextuality of configurations whose contexts are subspaces of dimension two and higher, (ii) non-existence of negative subspaces of dimension three and higher, (iii) considerably improved bounds for the contextuality degree of both elliptic and hyperbolic quadrics for ranks four, as well as for a particular subgeometry of the three-qubit space whose contexts are the lines of this space, (iv) proof for the non-contextuality of perpsets and, last but not least, (v) contextual nature of a distinguished subgeometry of a multi-qubit doily, called a two-spread, and computation of its contextuality degree.

12.Valuation of a Financial Claim Contingent on the Outcome of a Quantum Measurement

Authors:Lane P. Hughston, Leandro Sánchez-Betancourt

Abstract: We consider a rational agent who at time $0$ enters into a financial contract for which the payout is determined by a quantum measurement at some time $T>0$. The state of the quantum system is given by a known density matrix $\hat p$. How much will the agent be willing to pay at time $0$ to enter into such a contract? In the case of a finite dimensional Hilbert space, each such claim is represented by an observable $\hat X_T$ where the eigenvalues of $\hat X_T$ determine the amount paid if the corresponding outcome is obtained in the measurement. We prove, under reasonable axioms, that there exists a pricing state $\hat q$ which is equivalent to the physical state $\hat p$ on null spaces such that the pricing function $\Pi_{0T}$ takes the form $\Pi_{0T}(\hat X_T) = P_{0T}\,{\rm tr} ( \hat q \hat X_T) $ for any claim $\hat X_T$, where $P_{0T}$ is the one-period discount factor. By "equivalent" we mean that $\hat p$ and $\hat q$ share the same null space: thus, for any $|\xi \rangle \in \mathcal H$ one has $\langle \bar \xi | \hat p | \xi \rangle = 0$ if and only if $\langle \bar \xi | \hat q | \xi \rangle = 0$. We introduce a class of optimization problems and solve for the optimal contract payout structure for a claim based on a given measurement. Then we consider the implications of the Kochen-Specker theorem in such a setting and we look at the problem of forming portfolios of such contracts.

13.Amplifying a zeptonewton force with a single-ion nonlinear oscillator

Authors:Bo Deng, Moritz Göb, Benjamin A. Stickler, Max Masuhr, Kilian Singer, Daqing Wang

Abstract: Nonlinear mechanical resonators display rich and complex dynamics and are important in many areas of fundamental and applied sciences. In this letter, we show that a particle confined in a funnel-shaped potential features a Duffing-type nonlinearity due to the coupling between its radial and axial motion. Employing an ion trap platform, we study the nonlinear oscillation, bifurcation and hysteresis of a single calcium ion driven by radiation pressure. Harnessing the bistability of this atomic oscillator, we demonstrate a 20-fold enhancement of the signal from a zeptonewton-magnitude harmonic force through the effect of vibrational resonance. Our findings open up a range of possibilities for controlling and exploiting nonlinear phenomena of mechanical oscillators close to the quantum regime.

14.Frequency-domain engineering of bright squeezed vacuum for continuous-variable quantum information

Authors:Inbar Hurvitz, Aviv Karnieli, Ady Arie

Abstract: Multimode bright squeezed vacuum is a non-classical state of light hosting a macroscopic photon number while offering promising capacity for encoding quantum information in its spectral degree of freedom. Here, we employ an accurate model for parametric downconversion in the high-gain regime and use nonlinear holography to design quantum correlations of bright squeezed vacuum in the frequency domain. We propose the design of quantum correlations over two-dimensional lattice geometries that are all-optically controlled, paving the way toward continuous-variable cluster state generation on an ultrafast timescale. Specifically, we investigate the generation of a square cluster state in the frequency domain and calculate its covariance matrix and the quantum nullifier uncertainties, that exhibit squeezing below the vacuum noise level.

15.Lower bounds on the Approximate Stabilizer Rank: A Probabilistic Approach

Authors:Saeed Mehraban, Mehrdad Tahmasbi

Abstract: The approximate stabilizer rank of a quantum state is the minimum number of terms in any approximate decomposition of that state into stabilizer states. Bravyi and Gosset showed that the approximate stabilizer rank of a so-called "magic" state like $|T\rangle^{\otimes n}$, up to polynomial factors, is an upper bound on the number of classical operations required to simulate an arbitrary quantum circuit with Clifford gates and $n$ number of $T$ gates. As a result, an exponential lower bound on this quantity seems inevitable. Despite this intuition, several attempts using various techniques could not lead to a better than a linear lower bound on the "exact" rank of $|T\rangle^{\otimes n}$, meaning the minimal size of a decomposition that exactly produces the state. However, an "approximate" rank is more realistically related to the cost of simulating quantum circuits because exact rank is not robust to errors; there are quantum states with exponentially large exact ranks but constant approximate ranks even with arbitrarily small approximation parameters. No lower bound better than $\tilde \Omega(\sqrt n)$ has been known for the approximate rank. In this paper, we improve this lower bound to $\tilde \Omega (n)$ for a wide range of the approximation parameters. Our approach is based on a strong lower bound on the approximate rank of a quantum state sampled from the Haar measure and a step-by-step analysis of the approximate rank of a magic-state teleportation protocol to sample from the Haar measure.

16.Monitored non-adiabatic and coherent-controlled quantum unital Otto heat engines: First four cumulants

Authors:Abdelkader El Makouri, Abdallah Slaoui, Rachid Ahl Laamara

Abstract: Recently, measurement-based quantum thermal machines draw more attention in the field of quantum thermodynamics. However, the previous results on quantum Otto heat engines were either limited to special unital and non-unital channels in the bath stages, or a specific driving protocol at the work strokes and assuming the cycle being time-reversal symmetric i.e. $V^{\dagger}=U$ (or $V=U$). In this paper, we consider a single spin-1/2 quantum Otto heat engine, by first replacing one of the heat baths by an arbitrary unital channel and then we give the exact analytical expression of the characteristic function from which all the cumulants of heat and work emerge. We prove that under the effect of monitoring, $\nu_{2}>\nu_{1}$ is a necessary condition for positive work, either for a symmetric or asymmetric-driven Otto cycle. We trace this back to the negative role of projective measurement. We found that considering an arbitrary unital map would enhance the efficiency and the extracted work. Then we prove the system can never work as a refrigerator. This is forbidden by the second law of thermodynamics. Furthermore, going beyond the average we show that the ratio of the fluctuations of work and heat is lower and upper-bounded when the system is working as a heat engine. However, differently from the previous results in the literature we consider and analyze, skewness and kurtosis as well. We show that in the adiabatic regime, the skewness can be arbitrary and that kurtosis can not be below -2. Finally, we consider applying a specific unital map that plays the role of a heat bath in a coherently superposed manner and we show the role of the initial coherence of the control qubit on efficiency and the first four cumulants of work. In the non-adiabatic regime,...

17.QRAM: A Survey and Critique

Authors:Samuel Jaques, Arthur G. Rattew

Abstract: Quantum random-access memory (QRAM) is a mechanism to access data (quantum or classical) based on addresses which are themselves a quantum state. QRAM has a long and controversial history, and here we survey and expand arguments and constructions for and against. We use two primary categories of QRAM from the literature: (1) active, which requires external intervention and control for each QRAM query (e.g. the error-corrected circuit model), and (2) passive, which requires no external input or energy once the query is initiated. In the active model, there is a powerful opportunity cost argument: in many applications, one could repurpose the control hardware for the qubits in the QRAM (or the qubits themselves) to run an extremely parallel classical algorithm to achieve the same results just as fast. Escaping these constraints requires ballistic computation with passive memory, which creates an array of dubious physical assumptions, which we examine in detail. Considering these details, in everything we could find, all non-circuit QRAM proposals fall short in one aspect or another. We apply these arguments in detail to quantum linear algebra and prove that most asymptotic quantum advantage disappears with active QRAM systems, with some nuance related to the architectural assumptions. In summary, we conclude that cheap, asymptotically scalable passive QRAM is unlikely with existing proposals, due to fundamental limitations that we highlight. We hope that our results will help guide research into QRAM technologies that attempt to circumvent or mitigate these limitations. Finally, circuit-based QRAM still helps in many applications, and so we additionally provide a survey of state-of-the-art techniques as a resource for algorithm designers using QRAM.

18.Unbounded Quantum Advantage in One-Way Strong Communication Complexity of a Distributed Clique Labelling Relation

Authors:Sumit Rout, Nitica Sakharwade, Some Sankar Bhattacharya, Ravishankar Ramanathan, Paweł Horodecki

Abstract: We investigate the one-way zero-error classical and quantum communication complexities for a class of relations induced by a distributed clique labelling problem. We consider two variants: 1) the receiver outputs an answer satisfying the relation - the traditional communication complexity of relations (CCR) and 2) the receiver has non-zero probabilities of outputting every valid answer satisfying the relation (equivalently, the relation can be fully reconstructed), that we denote the strong communication complexity of the relation (S-CCR). We prove that for the specific class of relations considered here when the players do not share any resources, there is no quantum advantage in the CCR task for any graph. On the other hand, we show that there exist, classes of graphs for which the separation between one-way classical and quantum communication in the S-CCR task grow with the order of the graph, specifically, the quantum complexity is $O(1)$ while the classical complexity is $\Omega(\log m)$. Secondly, we prove a lower bound (that is linear in the number of cliques) on the amount of shared randomness necessary to overcome the separation in the scenario of fixed restricted communication and connect this to the existence of Orthogonal Arrays. Finally, we highlight some applications of this task to semi-device-independent dimension witnessing as well as to the detection of Mutually Unbiased Bases.

19.Using Entangled Generalized Coherent States for Photonic Quantum Metrology

Authors:Madhura Ghosh Dastidar, Aprameyan Desikan, Vidya Praveen Bhallamudi

Abstract: Quantum metrology aims at achieving enhanced performance in measuring unknown parameters by utilizing quantum resources. Thus, quantum metrology is an important application of quantum technologies. Photonic systems can implement these metrological tasks with simpler experimental techniques. We present a scheme for improved parameter estimation by introducing entangled generalized coherent states (EGCS) for photonic quantum metrology. These states show enhanced sensitivity beyond the classical and Heisenberg limits and prove to be advantageous as compared to the entangled coherent and NOON states. Further, we also propose a scheme for experimentally generating certain entangled generalized coherent states with current technology.

1.From entanglement to discord: a perspective based on partial transposition

Authors:Sun Liang-Liang, Zhou Xiang, Yu Sixia

Abstract: Here, we show that partial transposition, which is initially introduced to study entanglement, can also inspire many results on quantum discord including: (I) a discord criterion of spectrum invariant under partial transposition, stating that one state must contain discord if its spectrum is changed by the action of partial transposition, (II) an approach to estimate the geometric quantum discord and the one-way deficit based on the change of spectrum. To compare with entanglement theory, we also lower-bound the geometric quantum entanglement and the entanglement of relative entropy. Thus, on one hand, we illustrate an approach to specify and estimate discord based on partial transposition. On the other hand, we show that, entanglement and discord, two basic notions of nonclassical correlations, can be placed on the same ground such that their interplay and distinction can be illustrated in within a universal framework.

2.Non-Hermitian Casimir Effect of Magnons

Authors:Kouki Nakata, Kei Suzuki

Abstract: There has been a growing interest in non-Hermitian quantum mechanics. The key concepts of quantum mechanics are quantum fluctuations. Quantum fluctuations of quantum fields confined in a finite-size system induce the zero-point energy shift. This quantum phenomenon, the Casimir effect, is one of the most striking phenomena of quantum mechanics in the sense that there are no classical analogs and has been attracting much attention beyond the hierarchy of energy scales, ranging from elementary particle physics to condensed matter physics, together with photonics. However, the non-Hermitian extension of the Casimir effect and the application to spintronics have not yet been investigated enough, although exploring energy sources and developing energy-efficient nanodevices are its central issues. Here we fill this gap. By developing a magnonic analog of the Casimir effect into non-Hermitian systems, we show that this non-Hermitian Casimir effect of magnons is enhanced as the Gilbert damping constant (i.e., the energy dissipation rate) increases. When the damping constant exceeds a critical value, the non-Hermitian Casimir effect of magnons exhibits an oscillating behavior, including a beating one, as a function of the film thickness and is characterized by the exceptional point. Our result suggests that energy dissipation serves as a key ingredient of Casimir engineering.

3.Instantaneous and non-zero tunneling time regimes

Authors:Philip Caesar M. Flores, Dean Alvin L. Pablico, Eric A. Galapon

Abstract: We demonstrate how an operator-based theory of quantum time-of-arrival (TOA) reconciles the seemingly conflicting reports on the measured tunneling times. This is done by defining the barrier traversal time as the difference of the expectation values of the corresponding TOA-operators in the presence and absence of the barrier. We show that for an arbitrarily shaped potential barrier, there exists three traversal time regimes corresponding to full-tunneling, partial-tunneling, and \non-tunneling processes, which are determined by the relation between the the support of the incident wavepacket's momentum distribution $\tilde{\psi}(k)$, and shape of the barrier. The full-tunneling process occurs when the support of $\tilde{\psi}(k)$ is below the minimum height of the barrier, resulting to an instantaneous tunneling time. The partial-tunneling process occurs when the support or a segment of the support of $\tilde{\psi}(k)$ lies between the minimum and maximum height of the barrier. For this case, the particle does not "fully" tunnel through the entire barrier system resulting to a non-zero traversal time. The non-tunneling regime occurs when the support of $\tilde{\psi}(k)$ is above the maximum height of the barrier system, leading to a classical above-barrier traversal time. We argue that the zero and non-zero tunneling times measured in different attoclock experiments correspond to the full-tunneling and partial-tunneling processes, respectively.

4.Extension of the Watanabe-Sagawa-Ueda uncertainty relations to infinite-dimensional systems

Authors:Ryosuke Nogami

Abstract: Watanabe, Sagawa, and Ueda defined the measurement error of an observable and the disturbance to an observable by measurements for finite-dimensional systems on the basis of quantum estimation theory and derived uncertainty relation inequalities of error-error and error-disturbance types. This paper extend the Watanabe-Sagawa-Ueda uncertainty relations to infinite-dimensional systems employing the Fr\'echet derivative. We present a classical estimation theory and a quantum estimation theory, both of which are formulated for parameter spaces of infinite dimensions. An improvement in the derivation method makes the resulting uncertainty relation inequalities tighter than original ones.

5.Generation of multipartite entangled states based on double-longitudinal-mode cavity optomechanial systemGeneration of multipartite entangled states based on double-longitudinal-mode cavity optomechanial system

Authors:Xiaomin Liu, RongGuo Yang, Jing Zhang, Tiancai Zhang

Abstract: Optomechanical system is a promising platform to connect different notes of quantum networks, therefore, entanglement generated from it is also of great importance. In this paper, the parameter dependence of optomechanical and optical-optical entanglements generated from the double-longitudinal-mode cavity optomechanical system are discussed and two quadrapartite entanglement generation schemes based on such a system are proposed. Furthermore, 2N or 4N-partite entangled states can be obtained by coupling N cavities with N-1 beamsplitter(BS)s, and these schemes are scalable in increasing the partite number of entanglement. Certain ladder or linear structures are contained in the finally obtained entanglement structure, which can be applied in quantum computing or quantum networks in the future.

6.Non-classicality of squeezed non-Markovian processes

Authors:Mehdi Abdi, Moslem Zarei

Abstract: We study nonclassical effects in the dynamics of an open quantum system. The model involves a harmonic oscillator coupled to a reservoir of non-interacting harmonic oscillators. Different system-bath interaction schemes as well as reservoir states are considered. Particularly, the squeezed reservoirs coupled to the system through single and two quanta exchange processes are put in the spotlight. We investigate the quantumness conveyed to the system through the bath by computing a nonclassicality measure for different bath properties and when the memory effects are appreciable. The measure of nonclassicality is calculated for projective measurements both in the number state basis and a basis formed by a set of coherent states. Our results show that in both bases the measure exhibits characteristic features for each bath state and the form of its interaction with the system. Some of those features are independent from the measurement scheme (number or coherent), and thus, emergent from the bath and its interaction with the probe system. This allows for fingerprinting and identifying the environmental effects by tracking a given probe with appropriate measurements. Hence, may prove useful for distinguishing different sources of decoherence.

7.Conservation Laws for a Thermal Reservoir Model in Open Quantum Systems

Authors:Muhammad Al-Zafar Khan, Mervlyn Moodley, Francesco Petruccione

Abstract: We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic free particles in a thermal reservoir environment. Conservation laws are constructed subsequently using the Ibragimov method via a solution to the adjoint form of the equation of motion via its corresponding scalaing symmetry. A general computational framework for obtaining all conserved vectors is exhibited some triplets of conserved quantities are calculated in full.

8.Estimating properties of a quantum state by importance-sampled operator shadows

Authors:Naixu Guo, Patrick Rebentrost

Abstract: Measuring properties of quantum systems is a fundamental problem in quantum mechanics. We provide a very simple method for estimating expectation value of observables with an unknown quantum state. The idea is to sample the terms of the Pauli decomposition of observables proportionally to their importance. We call this technique operator shadow as a shorthand for the procedure preparing a sketch of an operator to estimate properties. For multiple local observables, the sample complexity of this method is better than the classical shadow technique only when the numbers of observables are small. However, if we want to estimate expectation values for linear combination of local observables, e.g., the energy of a local Hamiltonian, the sample complexity is better on all parameters.

9.Realizing fully reference-frame-independent quantum key distribution by exploiting quantum discord

Authors:Rong Wang, Chun-Mei Zhang

Abstract: Reference-frame-independent quantum key distribution was proposed to generate a string of secret keys without a shared reference frame. Based on the Bloch sphere, however, the security analysis in previous methods is only independent on azimuthal angle, while a reference frame is determined by both polar angle and azimuthal angle. Here, we propose a 3 \times 3 matrix whose singular values are independent on both polar angle and azimuthal angle, as well as take advantage of quantum discord, to realize a fully reference-frame-independent quantum key distribution. Furthermore, we numerically show that the performance of our method can reduce to the previous one if the key generation basis is calibrated.

10.Energy risk analysis with Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling

Authors:Kumar J. B. Ghosh, Kavitha Yogaraj, Gabriele Agliardi, Piergiacomo Sabino, Marina Fernández-Campoamor, Juan Bernabé-Moreno, Giorgio Cortiana, Omar Shehab, Corey O'Meara

Abstract: We generalize the Approximate Quantum Compiling algorithm into a new method for CNOT-depth reduction, which is apt to process wide target quantum circuits. Combining this method with state-of-the-art techniques for error mitigation and circuit compiling, we present a 10-qubit experimental demonstration of Iterative Amplitude Estimation on a quantum computer. The target application is the derivation of the Expected Value of contract portfolios in the energy industry. In parallel, we also introduce a new variant of the Quantum Amplitude Estimation algorithm which we call Dynamic Amplitude Estimation, as it is based on the dynamic circuit capability of quantum devices. The algorithm achieves a reduction in the circuit width in the order of the binary precision compared to the typical implementation of Quantum Amplitude Estimation, while simultaneously decreasing the number of quantum-classical iterations (again in the order of the binary precision) compared to the Iterative Amplitude Estimation. The calculation of the Expected Value, VaR and CVaR of contract portfolios on quantum hardware provides a proof of principle of the new algorithm.

11.Where are we heading with NISQ?

Authors:Olivier Ezratty

Abstract: In 2017, John Preskill defined Noisy Intermediate Scale Quantum (NISQ) computers as an intermediate step on the road to large scale error corrected fault-tolerant quantum computers (FTQC). The NISQ regime corresponds to noisy qubit quantum computers with the potential to solve actual problems of some commercial value faster than conventional supercomputers, or consuming less energy. Over five years on, it is a good time to review the situation. While rapid progress is being made with quantum hardware and algorithms, and many recent experimental demonstrations, no one has yet successfully implemented a use case matching the original definition of the NISQ regime. This paper investigates the space, fidelity and time resources of various NISQ algorithms and highlights several contradictions between NISQ requirements and actual as well as future quantum hardware capabilities. It then covers various techniques which could help like qubit fidelities improvements, various breeds of quantum error mitigation methods, analog/digital hybridization, using specific qubit types like multimode photons as well as quantum annealers and analog quantum computers (aka quantum simulators or programmable Hamiltonian simulators) which seem closer to delivering useful applications although they have their own mid to longer-term scalability challenges. Given all the constraints of these various solutions, it seems possible to expect some practical use cases for NISQ systems, but with a very narrow window before various scaling issues show up. Turning to the future, a scenario can be envisioned where NISQ will not necessarily be an intermediate step on the road to FTQC. Instead, the two may develop along different paths, due to their different requirements. This leaves open a key question on the trade-offs that may be necessary to make between qubit scale and qubit fidelities in future quantum computers designs.

12.Sensing orbital hybridization of graphene-diamond interface with a single spin

Authors:Yucheng Hao, Zhiping Yang, Zeyu Li, Xi Kong, Wenna Tang, Tianyu Xie, Shaoyi Xu, Xiangyu Ye, Pei Yu, Pengfei Wang, Ya Wang, Zhenhua Qiao, Libo Gao, Jian-Hua Jiang, Fazhan Shi, Jiangfeng Du

Abstract: Interfacial interactions are crucial in a variety of fields and can greatly affect the electric, magnetic, and chemical properties of materials. Among them, interface orbital hybridization plays a fundamental role in the properties of surface electrons such as dispersion, interaction, and ground states. Conventional measurements of electronic states at interfaces such as scanning tunneling microscopes are all based on electric interactions which, however, suffer from strong perturbation on these electrons. Here we unveil a new experimental detection of interface electrons based on the weak magnetic interactions between them and the nitrogen-vacancy (NV) center in diamond. With negligible perturbation on the interface electrons, their physical properties can be revealed by the NV spin coherence time. In our system, the interface interaction leads to significant decreases in both the density and coherence time of the electron spins at the diamond-graphene interface. Furthermore, together with electron spin resonance spectra and first-principle calculations, we can retrieve the effect of interface electron orbital hybridization. Our study opens a new pathway toward the microscopic probing of interfacial electronic states with weak magnetic interactions and provides a new avenue for future research on material interfaces.

13.Predicting RNA Secondary Structure on Universal Quantum Computer

Authors:Ji Jiang, Qipeng Yan, Ye Li, Yahui Chai, Min Lu, Ziwei Cui, Menghan Dou, Qingchun Wang, Yu-Chun Wu, Guo-Ping Guo

Abstract: It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while learning-based algorithms face challenges in obtaining high-quality training data. Recently, quantum annealer has rapidly predicted the folding of the secondary structure, highlighting that quantum computing is a promising solution to this problem. However, gate model algorithms for universal quantum computing are not available. In this paper, gate-based quantum algorithms will be presented, which are highly flexible and can be applied to various physical devices. Mapped all possible secondary structure to the state of a quadratic Hamiltonian, the whole folding process is described as a quadratic unconstrained binary optimization model. Then the model can be solved through quantum approximation optimization algorithm. We demonstrate the performance with both numerical simulation and experimental realization. Throughout our benchmark dataset, simulation results suggest that our quantum approach is comparable in accuracy to classical methods. For non-nested sequences, our quantum approach outperforms classical energy-based methods. Experimental results also indicate our method is robust in current noisy devices. It is the first instance of universal quantum algorithms being employed to tackle RNA folding problems, and our work provides a valuable model for utilizing universal quantum computers in solving RNA folding problems.

14.Asymmetric node placement in fiber-based quantum networks

Authors:Guus Avis, Robert Knegjens, Anders S. Sørensen, Stephanie Wehner

Abstract: Restrictions imposed by existing infrastructure can make it hard to ensure an even spacing between the nodes of future fiber-based quantum networks. We here investigate the negative effects of asymmetric node placement by considering separately the placement of midpoint stations required for heralded entanglement generation, as well as of processing-node quantum repeaters in a chain. For midpoint stations, we describe the effect asymmetry has on the time required to perform one entangling attempt, the success probability of such attempts, and the fidelity of the entangled states created. This includes accounting for the effects of chromatic dispersion on photon indistinguishability. For quantum-repeater chains we numerically investigate how uneven spacing between repeater nodes leads to bottlenecks, thereby increasing both the waiting time and the time states are stored in noisy quantum memory. We find that while the time required to perform one entangling attempt may increase linearly with the midpoint's asymmetry, the success probability and fidelity of heralded entanglement generation and the distribution time and error rate for repeater chains all have vanishing first derivatives with respect to the amount of asymmetry. This suggests resilience of quantum-network performance against small amounts of asymmetry.

15.Accelerating Quantum Algorithms with Precomputation

Authors:William J. Huggins, Jarrod R. McClean

Abstract: Real-world applications of computing can be extremely time-sensitive. It would be valuable if we could accelerate such tasks by performing some of the work ahead of time. Motivated by this, we propose a cost model for quantum algorithms that allows quantum precomputation; i.e., for a polynomial amount of "free" computation before the input to an algorithm is fully specified, and methods for taking advantage of it. We analyze two families of unitaries that are asymptotically more efficient to implement in this cost model than in the standard one. The first example of quantum precomputation, based on density matrix exponentiation, could offer an exponential advantage under certain conditions. The second example uses a variant of gate teleportation to achieve a quadratic advantage when compared with implementing the unitaries directly. These examples hint that quantum precomputation may offer a new arena in which to seek quantum advantage.

16.Many-Body Excited States with a Contracted Quantum Eigensolver

Authors:Scott E. Smart, Davis M. Welakuh, Prineha Narang

Abstract: Calculating ground and excited states is an exciting prospect for near-term quantum computing applications, and accurate and efficient algorithms are needed to assess viable directions. We develop an excited state approach based on the contracted quantum eigensolver (ES-CQE), which iteratively attempts to find a solution to a contraction of the Schr{\"o}dinger equation projected onto a subspace, and does not require a priori information on the system. We focus on the anti-Hermitian portion of the equation, leading to a two-body unitary ansatz. We investigate the role of symmetries, initial states, constraints, and overall performance within the context of the model rectangular ${\rm H}_4$ system. We show the ES-CQE achieves near-exact accuracy across the majority of states, covering regions of strong and weak electron correlation, while also elucidating challenging instances for two-body unitary ansatz.

1.A general method to construct mean field counter diabatic driving for a ground state search

Authors:Hiroshi Hayasaka, Takashi Imoto, Yuichiro Matsuzaki, Shiro Kawabata

Abstract: The counter diabatic (CD) driving has attracted much attention for suppressing non-adiabatic transition in quantum annealing (QA). However, it can be intractable to construct the CD driving in the actual experimental setup due to the non-locality of the CD dariving Hamiltonian and necessity of exact diagonalization of the QA Hamiltonian in advance. In this paper, using the mean field (MF) theory, we propose a general method to construct an approximated CD driving term consisting of local operators. We can efficiently construct the MF approximated CD (MFCD) term by solving the MF dynamics of magnetization using a classical computer. As an example, we numerically perform QA with MFCD driving for the spin glass model with transverse magnetic fields. We numerically show that the MF dynamics with MFCD driving is equivalent to the solution of the self-consistent equation in MF theory. Also, we clarify that a ground state of the spin glass model with transverse magnetic field can be obtained with high fidelity compared to the conventional QA without the CD driving. Moreover, we experimentally demonstrate our method by using a D-wave quantum annealer and obtain the experimental result supporting our numerical simulation.

2.Recognizing critical lines via entanglement in non-Hermitian systems

Authors:Keshav Das Agarwal, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, Aditi Sen De

Abstract: The non-Hermitian model exhibits counter-intuitive phenomena which are not observed in the Hermitian counterparts. To probe the competition between non-Hermitian and Hermitian interacting components of the Hamiltonian, we focus on a system containing non-Hermitian XY spin chain and Hermitian Kaplan-Shekhtman-Entin-Aharony (KSEA) interactions along with the transverse magnetic field. We show that the non-Hermitian model can be an effective Hamiltonian of a Hermitian XX spin-1/2 with KSEA interaction and a local magnetic field that interacts with local and non-local reservoirs. The analytical expression of the energy spectrum divides the system parameters into two regimes -- in one region, the strength of Hermitian KSEA interactions dominates over the imaginary non-Hermiticity parameter while in the other, the opposite is true. In the former situation, we demonstrate that the nearest-neighbor entanglement and its derivative can identify quantum critical lines with the variation of the magnetic field. In this domain, we determine a surface where the entanglement vanishes, similar to the factorization surface, known in the Hermitian case. On the other hand, when non-Hermiticity parameters dominate, we report the exceptional and critical points where the energy gap vanishes and illustrate that bipartite entanglement is capable of detecting these transitions as well. Going beyond this scenario, when the ground state evolves after a sudden quench with the transverse magnetic field, both rate function and the fluctuation of bipartite entanglement quantified via its second moment can detect critical lines generated without quenching dynamics.

3.Partial Transpose Moments, Principal Minors and Entanglement Detection

Authors:Mazhar Ali

Abstract: Recently, it has been shown that locally randomized measurements can be employed to get partial transpose moments of a density matrix [Elben A., {\it et al.} Phys. Rev. Lett. {\bf 125}, 200501 (2020)]. Consequently, two general entanglement detection methods were proposed based on partial transpose moments of a density matrix [Yu X-D., {\it et al.} Phys. Rev. Lett. {\bf 127}, 060504 (2021)]. In this context, a natural question arises that how partial transpose moments are related with entanglement and with well known idea of principal minors. In this work, we analytically demonstrate that for qubit-qubit quantum systems, partial transpose moments can be expressed as simple functions of principal minors. We expect this relation to exist for every bipartite quantum systems. In addition, we have extended the idea of PT-moments for tripartite qubit systems and have shown that PT-moments can only detect the whole range of being NPT for $GHZ$ and $W$ states mixed with white noise.

4.Null dimension witness based on single measurements

Authors:Josep Batle, Adam Bednorz

Abstract: We present a null witness, based on equality due to linear independence, of the dimension of a quantum system, discriminating real, complex and classical spaces. The witness involves only a single measurement with sufficiently many outcomes and prepared input states. In addition, for intermediate dimensions, the witness bounds saturate for a family of equiangular tight frames including symmetric informationally complete positive operator valued measures. Such a witness requires a minimum of resources, being robust against many practical imperfections. We also discuss errors due to finite statistics.

5.Global quantum thermometry based on the optimal biased bound

Authors:Shoukang Chang, Wei Ye, Xuan Rao, Huan Zhang, Liqing Huang, Mengmeng Luo, Yuetao Chen, Qiang Ma, Shaoyan Gao

Abstract: Thermometry is a fundamental parameter estimation problem which is crucial in the development process of natural sciences. One way to solve this problem is to the extensive used local thermometry theory, which makes use of the classical and quantum Cram\'er-Rao bound as benchmarks of thermometry precision. However, such a thermometry theory can only be used for decreasing temperature fluctuations around a known temperature value and hardly tackle the precision thermometry problem over a wide temperature range. For this reason, we derive two basic bounds on thermometry precision in the global setting and further show their thermometry performance by two specific applications, i.e., noninteracting spin-1/2 gas and a general N-level thermal equilibrium quantum probe.

6.Quantum coherence assisted dynamical phase transition

Authors:Bao-Ming Xu

Abstract: Quantum coherence will undoubtedly play a fundamental role in understanding of the dynamics of quantum many-body systems, thereby to reveal its genuine contribution is of great importance. In this paper, we specialize our discussions to the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state, and investigate the effects of quantum coherence on dynamical phase transition (DQPT). After quenching the strength of the transverse field, the effects of quantum coherence are studied by Fisher zeros and the rate function of Loschmidt echo. We find that quantum coherence not only recovers DQPT destroyed by thermal fluctuations, but also generates some entirely new DQPTs which are independent of equilibrium quantum critical point. We also find that Fisher zero cutting the imaginary axis is not sufficient to generate DQPT because it also requires the Fisher zeros to be tightly bound close enough to the neighborhood of the imaginary axis. It can be manifested that DQPTs are rooted in quantum fluctuations. This work sheds new light on the fundamental connection between quantum critical phenomena and quantum coherence.

7.Simultaneous preparation of two optical cat states based on a nondegenerate optical parametric amplifier

Authors:Dongmei Han, Na Wang, Meihong Wang, Xiaolong Su

Abstract: The optical cat state, known as the superposition of coherent states, has broad applications in quantum computation and quantum metrology. Increasing the number of optical cat states is crucial to implement complex quantum information tasks based on them. Here, we prepare two optical cat states simultaneously based on a nondegenerate optical parametric amplifier. By subtracting one photon from each of two squeezed vacuum states, two odd cat states with orthogonal superposition direction in phase space are prepared simultaneously, which have similar fidelity of 60% and amplitude of 1.2. Compared with the traditional method to generate two odd optical cat states based on two degenerate optical parametric amplifiers, only one nondegenerate optical parametric amplifier is applied in our experiment, which saves half of the quantum resource of nonlinear cavities. The presented results make a step toward preparing the four-component cat state, which has potential applications in fault-tolerant quantum computation.

8.Nonlocality of Deep Thermalization

Authors:Harshank Shrotriya, Wen Wei Ho

Abstract: We study the role of topology in governing deep thermalization, the relaxation of a local subsystem towards a maximally-entropic, uniform distribution of post-measurement states, upon observing the complementary subsystem in a local basis. Concretely, we focus on a class of (1+1)d systems exhibiting `maximally-chaotic' dynamics, and consider how the rate of the formation of such a universal wavefunction distribution depends on boundary conditions of the system. We find that deep thermalization is achieved exponentially quickly in the presence of either periodic or open boundary conditions; however, the rate at which this occurs is twice as fast for the former than for the latter. These results are attained analytically using the calculus of integration over unitary groups, and supported by extensive numerical simulations. Our findings highlight the nonlocal nature of deep thermalization, and clearly illustrates that the physics underlying this phenomenon goes beyond that of standard quantum thermalization, which only depends on the net build-up of entanglement between a subsystem and its complement.

9.Maximum Power of Coupled-Qubit Otto Engines

Authors:Jingyi Gao, Naomichi Hatano

Abstract: We put forward four schemes of coupled-qubit quantum Otto machine, a generalization of the single-qubit quantum Otto machine, based on work and heat transfer between an internal system consisting of a coupled pair of qubits and an external environment consisting of two heat baths and two work storages. The four schemes of our model are defined by the positions of attaching the heat baths, which play a key role in the power of the coupled-qubit engine. Firstly, for the single-qubit heat engine, we find a maximum-power relation, and the fact that its efficiency at the maximum power is equal to the Otto efficiency, which is greater than the Curzon-Ahlborn efficiency. Second, we compare the coupled-qubit engines to the single-qubit one from the point of view of achieving the maximum power based on the same energy-level change for work production, and find that the coupling between the two qubits can lead to greater powers but the system efficiency at the maximum power is lower than the single-qubit system's efficiency and the Curzon-Ahlborn efficiency.

10.Quantum interference induced magnon blockade and antibunching in a hybrid quantum system

Authors:Pooja Kumari Gupta, Sampreet Kalita, Amarendra K. Sarma

Abstract: In this work, we study the phenomena of quantum interference assisted magnon blockade and magnon antibunching in a weakly interacting hybrid ferromagnet-superconductor system. The magnon excitations in two yttrium iron garnet spheres are indirectly coupled to a superconducting qubit through microwave cavity modes of two mutually perpendicular cavities. We find that when one of the magnon mode is driven by a weak optical field, the destructive interference between more than two distinct transition pathways restricts simultaneous excitation of two magnons. We analyze the magnon correlations in the driven magnon mode for the case of zero detunings as well as finite detunings of the magnon modes and the qubit. We show that the magnon antibunching can be tuned by changing the magnon-qubit coupling strength ratio and the driving detuning. Our work proposes a possible scheme which have significant role in the construction of single magnon generating devices.

11.Errors in heralded circuits for linear optical entanglement generation

Authors:Reece D. Shaw, Alex E. Jones, Patrick Yard, Anthony Laing

Abstract: The heralded generation of entangled states underpins many photonic quantum technologies. As quantum error correction thresholds are determined by underlying physical noise mechanisms, a detailed and faithful characterization of resource states is required. Non-computational leakage, e.g. more than one photon occupying a dual-rail encoded qubit, is an error not captured by standard forms of state tomography, which postselect on photons remaining in the computational subspace. Here we use the continuous-variable (CV) formalism and first quantized state representation to develop a simulation framework that reconstructs photonic quantum states in the presence of partial distinguishability and resulting non-computational leakage errors. Using these tools, we analyze a variety of Bell state generation circuits and find that the five photon discrete Fourier transform (DFT) Bell state generation scheme [Phys Rev. Lett. 126 23054 (2021)] is most robust to such errors for near-ideal photons. Through characterization of a photonic entangling gate, we demonstrate how leakage errors prevent a modular characterization of concatenated gates using current tomographical procedures. Our work is a necessary step in revealing the true noise models that must be addressed in fault-tolerant photonic quantum computing architectures.

12.Quantum reliability

Authors:L. X. Cui, Y-M. Du, C. P. Sun

Abstract: The present study investigates the reliability of functioning systems that depend on quantum coherence. In contrast to the conventional notion of reliability in industry and technology, which is evaluated using probabilistic measurements of binary logical variables, quantum reliability is grounded in the quantum probability amplitude, or wave function, due to the interference between different system trajectories. A system of quantum storage with a fault-tolerance structure is presented to illustrate the definition and calculation of quantum reliability. Our findings reveal that quantum coherence alters the relationship between a system's reliability and that of its subsystems, compared to classical cases. This effect is particularly relevant for quantum complexes with multiple interacting subsystems that require a precise operation.

13.Beyond Gaussian Quantum Channels: A model case

Authors:Daniel Speed, Wenyang Lyu, Roman Schubert

Abstract: Gaussian quantum channels are well understood and have many applications, e.g., in Quantum Information Theory and in Quantum Optics. For more general quantum channels one can in general use semiclassical approximations or perturbation theory, but it is not easy to judge the accuracy of such methods. We study a relatively simple model case, where the quantum channel is generated by a Lindblad equation where one of the Lindblad operators is a multiple of the internal Hamiltonian, and therefore the channel is not Gaussian. For this model we can compute the characteristic function of the action of the channel on a Gaussian state explicitly and we can as well derive a representation of the propagator in an integral form. This allows us to compare the exact results with semiclassical approximations and perturbation theory and evaluate their accuracy. We finally apply these results to the study of the evolution of the von Neumann entropy of a state.

14.Combining the QAOA and HHL Algorithm to achieve a Substantial Quantum Speedup for the Unit Commitment Problem

Authors:Jonas Stein, Jezer Jojo, Afrah Farea, David Bucher, Philipp Altmann, Claudia Linnhoff-Popien

Abstract: In this paper, we propose a quantum algorithm to solve the unit commitment (UC) problem at least cubically faster than existing classical approaches. This is accomplished by calculating the energy transmission costs using the HHL algorithm inside a QAOA routine. We verify our findings experimentally using quantum circuit simulators in a small case study. Further, we postulate the applicability of the concepts developed for this algorithm to be used for a large class of optimization problems that demand solving a linear system of equations in order to calculate the cost function for a given solution.

15.Quantum Neural Network for Quantum Neural Computing

Authors:Min-Gang Zhou, Zhi-Ping Liu, Hua-Lei Yin, Chen-Long Li, Tong-Kai Xu, Zeng-Bing Chen

Abstract: Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model for quantum neural computing using (classically-controlled) single-qubit operations and measurements on real-world quantum systems with naturally occurring environment-induced decoherence, which greatly reduces the difficulties of physical implementations. Our model circumvents the problem that the state-space size grows exponentially with the number of neurons, thereby greatly reducing memory requirements and allowing for fast optimization with traditional optimization algorithms. We benchmark our model for handwritten digit recognition and other nonlinear classification tasks. The results show that our model has an amazing nonlinear classification ability and robustness to noise. Furthermore, our model allows quantum computing to be applied in a wider context and inspires the earlier development of a quantum neural computer than standard quantum computers.

16.On a paradox in quantum mechanics and its resolution

Authors:Padtarapan Banyadsin, Salvatore De Vincenzo

Abstract: Consider a free Schr\"odinger particle inside an interval with walls characterized by the Dirichlet boundary condition. Choose a parabola as the normalized state of the particle that satisfies this boundary condition. To calculate the variance of the Hamiltonian in that state, one needs to calculate the mean value of the Hamiltonian and that of its square. If one uses the standard formula to calculate these mean values, one obtains both results without difficulty, but the variance unexpectedly takes an imaginary value. If one uses the same expression to calculate these mean values but first writes the Hamiltonian and its square in terms of their respective eigenfunctions and eigenvalues, one obtains the same result as above for the mean value of the Hamiltonian but a different value for its square (in fact, it is not zero); hence, the variance takes an acceptable value. From whence do these contradictory results arise? The latter paradox has been presented in the literature as an example of a problem that can only be properly solved by making use of certain fundamental concepts within the general theory of linear operators in Hilbert spaces. Here, we carefully review those concepts and apply them in a detailed way to resolve the paradox. Our results are formulated within the natural framework of wave mechanics, and to avoid inconveniences that the use of Dirac's symbolic formalism could bring, we avoid the use of that formalism throughout the article. In addition, we obtain a resolution of the paradox in an entirely formal way without addressing the restrictions imposed by the domains of the operators involved. We think that the content of this paper will be useful to undergraduate and graduate students as well as to their instructors.

17.Quantum Optimized Centroid Initialization

Authors:Nicholas R. Allgood, Ajinkya Borle, Charles K. Nicholas

Abstract: One of the major benefits of quantum computing is the potential to resolve complex computational problems faster than can be done by classical methods. There are many prototype-based clustering methods in use today, and the selection of the starting nodes for the center points is often done randomly. Clustering often suffers from accepting a local minima as a valid solution when there are possibly better solutions. We will present the results of a study to leverage the benefits of quantum computing for finding better starting centroids for prototype-based clustering.

18.Information Reconciliation for High-Dimensional Quantum Key Distribution using Nonbinary LDPC codes

Authors:Ronny Mueller, Davide Bacco, Leif Katsou Oxenløwe, Søren Forchhammer

Abstract: Information Reconciliation is an essential part of Quantum Key distribution protocols that closely resembles Slepian-Wolf coding. The application of nonbinary LDPC codes in the Information Reconciliation stage of a high-dimensional discrete-variable Quantum Key Distribution setup is proposed. We model the quantum channel using a $q$-ary symmetric channel over which qudits are sent. Node degree distributions optimized via density evolution for the Quantum Key Distribution setting are presented, and we show that codes constructed using these distributions allow for efficient reconciliation of large-alphabet keys.

19.Quantum state preparation via engineered ancilla resetting

Authors:Daniel Alcalde Puente, Felix Motzoi, Tommaso Calarco, Giovanna Morigi, Matteo Rizzi

Abstract: In this theoretical investigation, we study the effectiveness of a protocol that incorporates periodic quantum resetting to prepare ground states of frustration-free parent Hamiltonians. This protocol uses a steering Hamiltonian that enables local coupling between the system and ancillary degrees of freedom. At periodic intervals, the ancillary system is reset to its initial state. For infinitesimally short reset times, the dynamics can be approximated by a Lindbladian whose steady state is the target state. For finite reset times, however, the spin chain and the ancilla become entangled between reset operations. To evaluate the performance of the protocol, we employ Matrix Product State simulations and quantum trajectory techniques, focusing on the preparation of the spin-1 Affleck-Kennedy-Lieb-Tasaki state. Our analysis considers convergence time, fidelity, and energy evolution under different reset intervals. Our numerical results show that ancilla system entanglement is essential for faster convergence. In particular, there exists an optimal reset time at which the protocol performs best. Using a simple approximation, we provide insights into how to optimally choose the mapping operators applied to the system during the reset procedure. Furthermore, the protocol shows remarkable resilience to small deviations in reset time and dephasing noise. Our study suggests that stroboscopic maps using quantum resetting may offer advantages over alternative methods, such as quantum reservoir engineering and quantum state steering protocols, which rely on Markovian dynamics.

20.Long-time relaxation of a finite spin bath linearly coupled to a qubit

Authors:Jukka P. Pekola, Bayan Karimi, Marco Cattaneo, Sabrina Maniscalco

Abstract: We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of $N$ spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime $N\gg 1$, assuming that the qubit-bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behavior is captured by an analytical approximation that makes use of the property $N\gg 1$ to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.

21.Synthetic $\mathbb{Z}_2$ gauge theories based on parametric excitations of trapped ions

Authors:O. Băzăvan, S. Saner, E. Tirrito, G. Araneda, R. Srinivas, A. Bermudez

Abstract: We present a detailed scheme for the implementation of $\mathbb{Z}_2$ gauge theories with dynamical bosonic matter using analog quantum simulators based on crystals of trapped ions. We introduce a versatile toolbox based on a state-dependent parametric excitation, which can be implemented using different interactions that couple the ions' internal qubit states to their motion, and induces a tunneling of the vibrational excitations of the crystal mediated by the trapped-ion qubits. To evaluate the feasibility of this toolbox, we perform numerical simulations of the considered schemes using realistic experimental parameters. This building block, when implemented with a single trapped ion, corresponds to a minimal $\mathbb{Z}_2$ gauge theory on a synthetic link where the qubit resides, playing the role of the gauge field. The vibrational excitations of the ion along different trap axes mimic the dynamical matter fields carrying a $\mathbb{Z}_2$ charge. We discuss how to generalise this minimal case to more complex settings by increasing the number of ions. We describe various possibilities which allow us to move from a single $\mathbb{Z}_2$ plaquette to full $\mathbb{Z}_2$ gauge chains. We present analytical expressions for the gauge-invariant dynamics and confinement, which are benchmarked using matrix product state simulations.

22.Minimal orthonormal bases for pure quantum state estimation

Authors:Leonardo Zambrano, Luciano Pereira, Aldo Delgado

Abstract: We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two bases are not sufficient to construct an informationally complete positive operator-valued measurement (IC-POVM) for pure states. We demonstrate our method using a binary tree structure, providing an algorithmic path for implementation. The performance of the method is evaluated through numerical simulations, showcasing its effectiveness for quantum state estimation.

23.QAOA-MC: Markov chain Monte Carlo enhanced by Quantum Alternating Operator Ansatz

Authors:Yuichiro Nakano, Hideaki Hakoshima, Kosuke Mitarai, Keisuke Fujii

Abstract: Quantum computation is expected to accelerate certain computational task over classical counterpart. Its most primitive advantage is its ability to sample from classically intractable probability distributions. A promising approach to make use of this fact is the so-called quantum-enhanced Markov chain Monte Carlo (MCMC) [D. Layden, et al., arXiv:2203.12497 (2022)] which uses outputs from quantum circuits as the proposal distributions. In this work, we propose the use of Quantum Alternating Operator Ansatz (QAOA) for quantum-enhanced MCMC and provide a strategy to optimize its parameter to improve convergence speed while keeping its depth shallow. The proposed QAOA-type circuit is designed to satisfy the specific constraint which quantum-enhanced MCMC requires with arbitrary parameters. Through our extensive numerical analysis, we find a correlation in certain parameter range between an experimentally measurable value, acceptance rate of MCMC, and the spectral gap of the MCMC transition matrix, which determines the convergence speed. This allows us to optimize the parameter in the QAOA circuit and achieve quadratic speedup in convergence. Since MCMC is used in various areas such as statistical physics and machine learning makes, this work represents an important step toward realizing practical quantum advantage with currently available quantum computers through quantum-enhanced MCMC.

24.Predictive Models from Quantum Computer Benchmarks

Authors:Daniel Hothem, Jordan Hines, Karthik Nataraj, Robin Blume-Kohout, Timothy Proctor

Abstract: Holistic benchmarks for quantum computers are essential for testing and summarizing the performance of quantum hardware. However, holistic benchmarks -- such as algorithmic or randomized benchmarks -- typically do not predict a processor's performance on circuits outside the benchmark's necessarily very limited set of test circuits. In this paper, we introduce a general framework for building predictive models from benchmarking data using capability models. Capability models can be fit to many kinds of benchmarking data and used for a variety of predictive tasks. We demonstrate this flexibility with two case studies. In the first case study, we predict circuit (i) process fidelities and (ii) success probabilities by fitting error rates models to two kinds of volumetric benchmarking data. Error rates models are simple, yet versatile capability models which assign effective error rates to individual gates, or more general circuit components. In the second case study, we construct a capability model for predicting circuit success probabilities by applying transfer learning to ResNet50, a neural network trained for image classification. Our case studies use data from cloud-accessible quantum computers and simulations of noisy quantum computers.

25.Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions

Authors:James Brown

Abstract: We show that chemically-accurate potential energy surfaces (PESs) can be generated from quantum computers by measuring the density along an adiabatic transition between different molecular geometries. In lieu of using phase estimation, the energy is evaluated by performing line-integration using the inverted TDDFT Kohn-Sham potential obtained from the time-varying densities. The accuracy of this method depends on the validity of the adiabatic evolution itself and the potential inversion process (which is theoretically exact but can be numerically unstable), whereas total evolution time is the defining factor for the precision of phase estimation. We examine the method with a one-dimensional system of two electrons for both the ground and first triplet state in first quantization, as well as the ground state of three- and four- electron systems in second quantization. It is shown that few accurate measurements can be utilized to obtain chemical accuracy across the full potential energy curve, with shorter propagation time than may be required using phase estimation for a similar accuracy. We also show that an accurate potential energy curve can be calculated by making many imprecise density measurements (using few shots) along the time evolution and smoothing the resulting density evolution. We discuss how one can generate full PESs using either sparse grid representations or machine learning density functionals where it is known that training the functional using the density (along with the energy) generates a more transferable functional than only using the energy. Finally, it is important to note that the method is able to classically provide a check of its own accuracy by comparing the density resulting from a time-independent Kohn-Sham calculation using the inverted potential, with the measured density.

1.The Potential Inversion Theorem

Authors:Alec Shelley, Henry Hunt

Abstract: If the potential energy in a nearest neighbor tight binding model is flipped, we show that the time evolution of the wavefunction probability is conserved as long as the initial conditions only occupy even lattice sites or odd lattice sites and are real up to a global phase. This means that positive potentials trap particles just as well as negative potentials. Generalizations of this potential inversion theorem are discussed, and it is found that wavefunction probability evolution is conserved for these initial conditions for any transformation which flips the sign of all odd-distance hopping terms or all even-distance hopping terms. This predicts that electron pairs time evolve like positronium and therefore form bound states. We show a mapping of any lattice spin model onto a lattice hopping model and discuss general symmetries of these spin models using the potential inversion theorem.

2.Monogamy of entanglement for tripartite systems

Authors:Xue-Na Zhu, Gui Bao, Zhi-Xiang Jin, Shao-Ming Fei

Abstract: We study the monogamy of arbitrary quantum entanglement measures $E$ for tripartite quantum systems. Both sufficient and necessary conditions for $E$ to be monogamous in terms of the $\alpha$th power of $E$ are explicitly derived. It is shown that such monogamy of a entanglement measure $E$ only depends on the boundedness of the solution set of certain equations. Moreover, the monogamy conditions have been also obtained with respect to certain subsets of quantum states for a given quantum correlation. Detailed examples are given to illustrate our results.

3.A Full Quantum Generative Adversarial Network Model for High Energy Physics Simulations

Authors:Florian Rehm, Sofia Vallecorsa, Michele Grossi, Kerstin Borras, Dirk Krücker

Abstract: The prospect of quantum computing with a potential exponential speed-up compared to classical computing identifies it as a promising method in the search for alternative future High Energy Physics (HEP) simulation approaches. HEP simulations, such as employed at the Large Hadron Collider at CERN, are extraordinarily complex and require an immense amount of computing resources in hardware and time. For some HEP simulations, classical machine learning models have already been successfully developed and tested, resulting in several orders of magnitude speed-up. In this research, we proceed to the next step and explore whether quantum computing can provide sufficient accuracy, and further improvements, suggesting it as an exciting direction of future investigations. With a small prototype model, we demonstrate a full quantum Generative Adversarial Network (GAN) model for generating downsized eight-pixel calorimeter shower images. The advantage over previous quantum models is that the model generates real individual images containing pixel energy values instead of simple probability distributions averaged over a test sample. To complete the picture, the results of the full quantum GAN model are compared to hybrid quantum-classical models using a classical discriminator neural network.

4.A Practitioner's Guide to Quantum Algorithms for Optimisation Problems

Authors:Benjamin C. B. Symons, David Galvin, Emre Sahin, Vassil Alexandrov, Stefano Mensa

Abstract: Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP-hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for noisy intermediate scale quantum devices. Two main paradigms for quantum hardware are then discussed: quantum annealing and gate-based quantum computing. While quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples. The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation (QAO) algorithm and the quantum alternating operator ansatz (QAOA) framework, are discussed in detail. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.

5.A perspective on Lindblad's Non-Equilibrium Entropy

Authors:Erik Aurell, Ryoichi Kawai

Abstract: G\"oran Lindblad in 1983 published a monograph on non-equilibrium thermodynamics. We here summarize the contents of this book, and provide a perspective on its relation to later developments in statistical physics and quantum physics. We high-light two aspects. The first is the idea that while all unitaries can be allowed in principle, different theories result from limiting which unitary evolutions are realized in the real world. The second is that Lindblad's proposal for thermodynamic entropy (as opposed to information-theoretic entropy) foreshadows much more recent investigations into optimal quantum transport which is a current research focus in several fields.

6.On the consistency of relative facts

Authors:Eric G. Cavalcanti, Andrea Di Biagio, Carlo Rovelli

Abstract: Lawrence et al. have presented an argument purporting to show that ``relative facts do not exist'' and, consequently, ``Relational Quantum Mechanics is incompatible with quantum mechanics''. The argument is based on a GHZ-like contradiction between constraints satisfied by measurement outcomes in an extended Wigner's friend scenario. Here we present a strengthened version of the argument, and show why, contrary to the claim by Lawrence et al., these arguments do not contradict the consistency of a theory of relative facts. Rather, considering this argument helps clarify how one should not think about a theory of relative facts, like RQM.

7.A resource-efficient quantum-classical hybrid algorithm for energy gap evaluation

Authors:Yongdan Yang, Ying Li, Xiaosi Xu, Xiao Yuan

Abstract: Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap between two eigenstates. Hence, how to efficiently solve the energy gap becomes an important motive for researching new quantum algorithms. In this work, we propose a hybrid non-variational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation to evaluate the energy gap of a general quantum many-body system. Compared to conventional approaches, our algorithm does not require controlled real-time evolution, thus making its implementation much more experimental-friendly. Since our algorithm is non-variational, it is also free from the "barren plateaus" problem. To verify the efficiency of our algorithm, we conduct numerical simulations for the Heisenberg model and molecule systems on a classical emulator.

8.Spatial correlations in the qubit properties of D-Wave 2000Q measured and simulated qubit networks

Authors:Jessica Park, Susan Stepney, Irene D'Amico

Abstract: We show strong positive spatial correlations in the qubits of a D-Wave 2000Q quantum annealing chip that are connected to qubits outside their own unit cell. By simulating the dynamics of spin networks, we then show that correlation between nodes is affected by a number of factors. The different connectivity of qubits within the network means that information transfer is not straightforward even when all the qubit-qubit couplings have equal weighting. The similarity between connected nodes is further changed when the couplings' strength is scaled according to the physical length of the connections (here to simulate dipole-dipole interactions). This highlights the importance of understanding the architectural features and potentially unprogrammed interactions/connections that can divert the performance of a quantum system away from the idealised model of identical qubits and couplings across the chip.

9.Detecting high-dimensional entanglement in cold-atom quantum simulators

Authors:Niklas Euler, Martin Gärttner

Abstract: Quantum entanglement has been identified as a crucial concept underlying many intriguing phenomena in condensed matter systems such as topological phases or many-body localization. Recently, instead of considering mere quantifiers of entanglement like entanglement entropy, the study of entanglement structure in terms of the entanglement spectrum has shifted into the focus leading to new insights into fractional quantum Hall states and topological insulators, among others. What remains a challenge is the experimental detection of such fine-grained properties of quantum systems. The development of protocols for detecting features of the entanglement spectrum in cold atom systems, which are one of the leading platforms for quantum simulation, is thus highly desirable and will open up new avenues for experimentally exploring quantum many-body physics. Here we present a method to bound the width of the entanglement spectrum, or entanglement dimension, of cold atoms in lattice geometries, requiring only measurements in two experimentally accessible bases and utilizing ballistic time-of-flight (ToF) expansion. Building on previous proposals for entanglement certification for photon pairs, we first consider entanglement between two atoms of different atomic species and later generalize to higher numbers of atoms per species and multispecies configurations showing multipartite high-dimensional entanglement. Through numerical simulations we show that our method is robust against typical experimental noise effects and thus will enable high-dimensional entanglement certification in systems of up to 8 atoms using currently available experimental techniques.

10.A Feasible Semi-quantum Private Comparison Based on Entanglement Swapping of Bell States

Authors:Chong-Qiang Ye, Jian Li, Xiu-Bo Chen, Yanyan Hou

Abstract: Semi-quantum private comparison (SQPC) enables two classical users with limited quantum capabilities to compare confidential information using a semi-honest third party (TP) with full quantum power. However, entanglement swapping, as an important property of quantum mechanics in previously proposed SQPC protocols is usually neglected. In this paper, we propose a novel SQPC protocol based on the entanglement swapping of Bell states, where two classical users do not require additional implementation of the semi-quantum key distribution protocol to ensure the security of their private data. Security analysis shows that our protocol is resilient to both external and internal attacks. To verify the feasibility and correctness of the proposed SQPC protocol, we design and simulate the corresponding quantum circuits using IBM Qiskit. Finally, we compare and discuss the proposed protocol with previous similar work. The results reveal that our protocol maintains high qubit efficiency, even when entanglement swapping is employed. Consequently, our proposed protocol may have broader applicability in semi-quantum environments.

11.Verification of Continuous-Variable Quantum Memories

Authors:Paolo Abiuso

Abstract: A proper quantum memory is argued to consist in a quantum channel which cannot be simulated with a measurement followed by classical information storage and a final state preparation, i.e. an entanglement breaking (EB) channel. The verification of quantum memories (non-EB channels) is a task in which an honest user wants to test the quantum memory of an untrusted, remote provider. This task is inherently suited for the class of protocols with trusted quantum inputs, sometimes called measurement-device-independent (MDI) protocols. Here, we study the MDI certification of non-EB channels in continuous variable (CV) systems. We provide a simple witness based on adversarial metrology, and describe an experimentally friendly protocol that can be used to verify all non Gaussian incompatibility breaking quantum memories. Our results can be tested with current technology and can be applied to test other devices resulting in non-EB channels, such as CV quantum transducers and transmission lines.

12.Visualizing Entanglement, Measurements and Unitary Operations in multi-Qubit Systems

Authors:Jonas Bley, Eva Rexigel, Alda Arias, Nikolas Longen, Lars Krupp, Maximilian Kiefer-Emmanouilidis, Paul Lukowicz, Anna Donhauser, Stefan Küchemann, Jochen Kuhn, Artur Widera

Abstract: In the field of quantum information science and technology, the representation and visualization of quantum states and processes are essential for both research and education. In this context, a focus especially lies on ensembles of few qubits. While powerful representations exist for single-qubit illustrations, such as the infamous Bloch sphere, similar visualizations to intuitively understand quantum correlations or few-body entanglement are scarce. Here, we present the dimensional circle notation as a representation of such ensembles, adapting the so-called circle notation of qubits. The $n$-particle system is represented in an $n$-dimensional space, and the mathematical conditions for separability lead to symmetry conditions of the quantum state visualized. This notation promises significant potential for conveying nontrivial quantum properties and processes such as entanglement, measurements and unitary operations in few-qubit systems to a broader audience, and it could enhance understanding of these concepts beyond education as a bridge between intuitive quantum insight and formal mathematical descriptions.

13.Local geometry and quantum geometric tensor of mixed states

Authors:Xu-Yang Hou, Zheng Zhou, Xin Wang, Hao Guo, Chih-Chun Chien

Abstract: The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum states via the density matrix and its purification. The unique gauge-invariant QGT of mixed states is derived, whose real part is the Bures metric and its imaginary part is the Uhlmann form. In contrast to the imaginary part of the pure-state QGT that is proportional to the Berry curvature, the Uhlmann form vanishes identically for ordinary physical processes. Moreover, there exists a Pythagorean-like equation that links different local distances, reflecting the underlying fibration. The Bures metric reduces to the Fubini-Study metric as temperature approaches zero if the eigenvalues of the density matrix do not change during the process, establishing a correspondence between the distances of pure and mixed states. To complete the comprehensive view of the geometry and QGT of mixed states, we present two examples contrasting different aspects of their local geometries.

14.Shielding collisions of ultracold CaF molecules with static electric fields

Authors:Bijit Mukherjee, Matthew D. Frye, C. Ruth Le Sueur, Michael R. Tarbutt, Jeremy M. Hutson

Abstract: We study collisions of ultracold CaF molecules in strong static electric fields. Such fields allow the creation of long-range barriers in the interaction potential, which prevent the molecules reaching the short-range region where inelastic and other loss processes are likely to occur. We carry out coupled-channel calculations of rate coefficients for elastic scattering and loss. We develop an efficient procedure for including energetically well-separated rotor functions in the basis set via a Van Vleck transformation. We show that shielding is particularly efficient for CaF and allows the rate of 2-body loss processes to be reduced by a factor of $10^7$ or more at a field of 23 kV/cm. The loss rates remain low over a substantial range of fields. Electron and nuclear spins cause strong additional loss in some small ranges of field, but have little effect elsewhere. The results pave the way for evaporative cooling of CaF towards quantum degeneracy.

15.The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States

Authors:Adam Burchardt, Frederik Hahn

Abstract: This paper introduces the foliage partition, an easy-to-compute LC-invariant for graph states, of computational complexity $\mathcal{O}(n^3)$ in the number of qubits. Inspired by the foliage of a graph, our invariant has a natural graphical representation in terms of leaves, axils, and twins. It captures both, the connection structure of a graph and the $2$-body marginal properties of the associated graph state. We relate the foliage partition to the size of LC-orbits and use it to bound the number of LC-automorphisms of graphs. We also show the invariance of the foliage partition when generalized to weighted graphs and qudit graph states.

16.Probing spectral features of quantum many-body systems with quantum simulators

Authors:Jinzhao Sun, Lucia Vilchez-Estevez, Vlatko Vedral, Andrew T. Boothroyd, M. S. Kim

Abstract: The efficient probing of spectral features of quantum many-body systems is important for characterising and understanding the structure and dynamics of quantum materials. In this work, we establish a framework for probing the excitation spectrum of quantum many-body systems with quantum simulators. Our approach effectively realises a spectral detector by processing the dynamics of observables with time intervals drawn from a defined probability distribution, which only requires native time evolution governed by the Hamiltonian without any ancilla. The critical element of our method is the engineered emergence of frequency resonance such that the excitation spectrum can be probed. We show that the time complexity for transition energy estimation has a logarithmic dependence on simulation accuracy, and discuss the noise e robustness of our spectroscopic method. We present simulation results for the spectral features of typical quantum systems, including quantum spins, fermions and bosons. We experimentally demonstrate how spectroscopic features of spin lattice models can be probed with IBM quantum devices.

1.Quantum-enhanced optical beat-note detection beyond 3-dB noise penalty of image band

Authors:Keitaro Anai, Yutaro Enomoto, Hiroto Omura, Koji Nagano, Kiwamu Izumi, Mamoru Endo, Shuntaro Takeda

Abstract: Optical beat-note detection with two beams at different frequencies is a key sensing technology for various spatial/temporal measurements. However, its sensitivity is inherently susceptible to shot noise due to the extra shot-noise contamination from the image band known as the 3-dB noise penalty, as well as the unavoidable optical power constraints at detectors. Here, we propose a method to remove shot noise from all relevant bands including the extra noise by using squeezed light. We also demonstrate beyond-3-dB noise reduction experimentally. Our work should boost the sensitivity of various spatial/temporal measurements beyond the current limitations.

2.Superconducting wide strip photon detector with high critical current bank structure

Authors:Masahiro Yabuno, Fumihiro China, Hirotaka Terai, Shigehito Miki

Abstract: Superconducting strip single-photon detectors offer excellent photon detection performance and are indispensable tools for cutting-edge optical science and technologies, including photonic quantum computation and quantum networks. Ultra-wide superconducting strips with widths of tens of micrometers are desirable to achieve high polarization-independent detection efficiency using a simple straight strip. However, biasing the ultra-wide strip with sufficient superconducting current to make it sensitive to infrared photons is challenging. The main difficulty is maldistribution of the superconducting current in the strip, which generates excessive intrinsic dark counts. Here, we present a novel superconducting wide strip photon detector (SWSPD) with a high critical current bank (HCCB) structure. This HCCB structure enables suppression of the intrinsic dark counts and sufficient superconducting current biasing of the wide strip. We have experimentally demonstrated a polarization-independent system detection efficiency of ~78% for 1550 nm wavelength photons and a system dark count rate of ~80 cps using a 20-${\mu}$m-wide SWSPD with the HCCB structure. Additionally, fast jitter of 29.8 ps was achieved. The photolithographically manufacturable ultra-wide SWSPD with high efficiency, low dark count, and fast temporal resolution paves the way toward the development of large-scale optical quantum technologies, which will require enormous numbers of ultimate-performance single-photon detectors.

3.Parallelizing Quantum-Classical Workloads: Profiling the Impact of Splitting Techniques

Authors:Tuhin Khare, Ritajit Majumdar, Rajiv Sangle, Anupama Ray, Padmanabha Venkatagiri Seshadri, Yogesh Simmhan

Abstract: Quantum computers are the next evolution of computing hardware. Quantum devices are being exposed through the same familiar cloud platforms used for classical computers, and enabling seamless execution of hybrid applications that combine quantum and classical components. Quantum devices vary in features, e.g., number of qubits, quantum volume, CLOPS, noise profile, queuing delays and resource cost. So, it may be useful to split hybrid workloads with either large quantum circuits or large number of quantum circuits, into smaller units. In this paper, we profile two workload splitting techniques on IBM's Quantum Cloud: (1) Circuit parallelization, to split one large circuit into multiple smaller ones, and (2) Data parallelization to split a large number of circuits run on one hardware to smaller batches of circuits run on different hardware. These can improve the utilization of heterogenous quantum hardware, but involve trade-offs. We evaluate these techniques on two key algorithmic classes: Variational Quantum Eigensolver (VQE) and Quantum Support Vector Machine (QSVM), and measure the impact on circuit execution times, pre- and post-processing overhead, and quality of the result relative to a baseline without parallelization. Results are obtained on real hardware and complemented by simulations. We see that (1) VQE with circuit cutting is ~39\% better in ground state estimation than the uncut version, and (2) QSVM that combines data parallelization with reduced feature set yields upto 3x improvement in quantum workload execution time and reduces quantum resource use by 3x, while providing comparable accuracy. Error mitigation can improve the accuracy by ~7\% and resource foot-print by ~4\% compared to the best case among the considered scenarios.

4.A comparative study of higher-order nonclassicalities of photon-added-then-subtracted and photon-subtracted-then-added quantum states

Authors:Deepak, Arpita Chatterjee

Abstract: In the present paper, we have studied the higher as well as the lower-order nonclassicalities of photon-added-then-subtracted and photon-subtracted-then-added thermal and even coherent states. Different criteria such as Mandel's function ($Q_M^{(l)}$), higher-order antibunching ($d_h^{(l-1)}$), sub-Poissonian photon statistics ($D_h^{(l-1)}$), higher-order squeezing ($S^{(l)}$), Husimi function ($Q$), Agarwal-Tara criteria ($A_3$) and Klyshko's condition ($B(m)$) are used to witness the nonclassical feature of these states. Many of these conditions established that the considered states are highly nonclassical. It is also realized that the non-Gaussian photon-addition-then-subtraction operation is preferred over the photon-subtraction-then-addition for developing nonclassicality.

5.Quantum annealing for continuous-variable optimization: How is it effective?

Authors:Shunta Arai, Hiroki Oshiyama, Hidetoshi Nishimori

Abstract: The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function with a rugged energy landscape. After domain-wall encoding to map a continuous variable to discrete Ising variables, we first benchmark the performance of the real hardware, the D-Wave 2000Q, against several state-of-the-art classical optimization algorithms designed for continuous-variable problems to find that the D-Wave 2000Q matches the classical algorithms in a limited domain of computation time. Beyond this domain, the classical global optimization algorithms outperform the quantum device. Next, we examine several optimization algorithms that are applicable to the Ising formulation of the problem, such as the TEBD (time-evolving block decimation) to simulate ideal coherent quantum annealing, simulated annealing, simulated quantum annealing, and spin-vector Monte Carlo. The data show that TEBD's coherent quantum annealing achieves far better results than the other approaches, in particular demonstrating the effectiveness of coherent tunneling. From these two types of benchmarks, we conclude that the hardware realization of quantum annealing has the potential to significantly outperform the best classical algorithms if thermal noise and other imperfections are sufficiently suppressed and the device operates coherently, as demonstrated in recent short-time quantum simulations.

6.Mapping quantum circuits to modular architectures with QUBO

Authors:Medina Bandic, Luise Prielinger, Jonas Nüßlein, Anabel Ovide, Santiago Rodrigo, Sergi Abadal, Hans van Someren, Gayane Vardoyan, Eduard Alarcon, Carmen G. Almudever, Sebastian Feld

Abstract: Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled quantum bits that can communicate via quantum-coherent and classical links. In multi-core architectures, it is crucial to minimize the amount of communication between cores when executing an algorithm. Therefore, mapping a quantum circuit onto a modular architecture involves finding an optimal assignment of logical qubits (qubits in the quantum circuit) to different cores with the aim to minimize the number of expensive inter-core operations while adhering to given hardware constraints. In this paper, we propose for the first time a Quadratic Unconstrained Binary Optimization (QUBO) technique to encode the problem and the solution for both qubit allocation and inter-core communication costs in binary decision variables. To this end, the quantum circuit is split into slices, and qubit assignment is formulated as a graph partitioning problem for each circuit slice. The costly inter-core communication is reduced by penalizing inter-core qubit communications. The final solution is obtained by minimizing the overall cost across all circuit slices. To evaluate the effectiveness of our approach, we conduct a detailed analysis using a representative set of benchmarks having a high number of qubits on two different multi-core architectures. Our method showed promising results and performed exceptionally well with very dense and highly-parallelized circuits that require on average 0.78 inter-core communications per two-qubit gate.

7.Bounds on positive operator-valued measure based coherence of superposition

Authors:Meng-Li Guo, Jin-Min Liang, Bo Li, Shao-Ming Fei, Zhi-Xi Wang

Abstract: Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the $l_1$ norm of coherence, the robustness of coherence and the Tsallis relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition. Our results can be used to estimate range of quantum coherence of superposed states. Detailed examples are presented to verify our analytical bounds.

8.Spontaneous localisation from a coarse-grained deterministic and non-unitary dynamics

Authors:Kartik Kakade, Avnish Singh, Tejinder P. Singh

Abstract: Collapse of the wave function appears to violate the quantum superposition principle as well as deterministic evolution. Objective collapse models propose a dynamical explanation for this phenomenon, by making a stochastic non-unitary and norm-preserving modification to the Schr\"odinger equation. In the present article we ask how a quantum system evolves under a {\it deterministic} and non-unitary but norm-preserving evolution? We show using a simple two-qubit model that under suitable conditions, quantum linear superposition is broken, with the system predictably driven to one or the other alternatives. If this deterministic dynamics is coarse-grained and observed over a lower time resolution, the outcomes appear random while obeying the Born probability rule. Our analysis hence throws light on the distinct roles of non-unitarity and of stochasticity in objective collapse models.

9.Properties of a smooth, dense, invariant domain for singular potential Schroedinger operators

Authors:Thomas Thiemann

Abstract: Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it would be desirable to have at one's disposal an explicit basis spanning a dense and invariant domain for such types of Schr\"odinger operators, for instance stationary perturbation theory or the Raleigh-Ritz method. Here we make the observation, that not only a such basis can indeed be provided but that in addition relevant matrix elements and inner products can be computed analytically in closed form, thus providing the required data e.g. for an analytical Gram-Schmid orthonormalisation.

10.Fast, high-fidelity addressed single-qubit gates using efficient composite pulse sequences

Authors:A. D. Leu, M. F. Gely, M. A. Weber, M. C. Smith, D. P. Nadlinger, D. M. Lucas

Abstract: We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for $^{43}\text{Ca}^{+}$ hyperfine ''atomic clock'' qubits in a cryogenic (100K) surface trap. For a single qubit, we benchmark an error of $1.5$ $\times$ $10^{-6}$ per Clifford gate (implemented using $600~\text{ns}$ $\pi/2$-pulses). For two qubits in the same trap zone (ion separation $5~\mu\text{m}$), we use a spatial microwave field gradient, combined with an efficient 4-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error $3.4$ $\times$ $10^{-5}$ per logical gate.

11.An alternative foundation of quantum mechanics

Authors:Inge S. Helland

Abstract: A new approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an actor to assign numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an actor or to some communicating actors. Group actions are defined on these variables, and group representation theory is the basis for developing the Hilbert space formalism. Operators corresponding to accessible conceptual variables are derived, and in the discrete case it is argued that the possible physical values are the eigenvalues of these operators. The interpretation of quantum states (or eigenvector spaces) implied by this approach is as focused questions to nature together with sharp answers to those questions. The questions may be complementary in the sense defined by Bohr. The focus of the paper is the proposed foundation of quantum theory. It is shown here that the groups and transformation needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably. It is my view that the discussion on the interpretation of quantum mechanics should come after a thorough treatment of the foundation issue. The interpretation proposed here may be called a general epistemic interpretation of quantum theory. It is similar in some respects to QBism, can also be seen as a concrete implementation of aspects of Rovelli's Relational Quantum Mechanics, and has a relationship to several other interpretations. It is proposed that quantum state vectors should be limited to vectors that are eigenvectors of some physically meaningful operator. Consequences of this are sketched for some so-called quantum paradoxes.

12.The existence and unambiguity of the principal axis system of the EPR tensors

Authors:Stanislav Komorovsky

Abstract: Although the role of the electron paramagnetic resonance (EPR) g-tensor and hyperfine coupling tensor in the EPR effective spin Hamiltonian is discussed extensively in many textbooks, certain aspects of the theory are missing. In this text we will cover those gaps and thus provide a comprehensive theory about the existence of principal axes of the EPR tensors. However, an important observation is that both g- and a-tensors have two sets of principal axes -- one in the real and one in the fictitious spin space -- and, in fact, are not tensors. Moreover, we present arguments based on the group theory why only eigenvalues of the G-tensor, $\mb{G} = \mb{g}\mb{g}^{\!\mathsf{T}}$, and the sign of the determinant of the g-tensor are observable quantities (an analogical situation also holds for the hyperfine coupling tensor). We keep the number of assumptions to a minimum and thus the theory is applicable in the framework of the Dirac--Coulomb--Breit Hamiltonian and for any spatial symmetry of the system.

13.Quantum Circuits Noise Tailoring from a Geometric Perspective

Authors:Junkai Zeng, Yong-Ju Hai, Hao Liang, Xiu-Hao Deng

Abstract: Quantum errors subject to noisy environments remain a major obstacle to advancing quantum information technology. Solutions to this issue include robust quantum control at the pulse level and error correction or mitigation techniques at the circuit level. We develop a geometric method to unify the treatments of noises at both levels to understand noisy dynamics and reduce errors. We illustrate the error's random walk in the geometric space to explain how coherent noises are tailored into stochastic Pauli errors by randomized compiling. We obtain analytical formulas for the noise parameters and show how robust quantum control techniques can further improve circuit fidelity. We demonstrate the efficacy of our approach using numerical simulations, showcasing its potential for advancing quantum information processing.

14.Optimal Entanglement Distillation Policies for Quantum Switches

Authors:Vivek Kumar, Nitish K. Chandra, Kaushik P. Seshadreesan, Alan Scheller-Wolf, Sridhar Tayur

Abstract: In an entanglement distribution network, the function of a quantum switch is to generate elementary entanglement with its clients followed by entanglement swapping to distribute end-to-end entanglement of sufficiently high fidelity between clients. The threshold on entanglement fidelity is any quality-of-service requirement specified by the clients as dictated by the application they run on the network. We consider a discrete-time model for a quantum switch that attempts generation of fresh elementary entanglement with clients in each time step in the form of maximally entangled qubit pairs, or Bell pairs, which succeed probabilistically; the successfully generated Bell pairs are stored in noisy quantum memories until they can be swapped. We focus on establishing the value of entanglement distillation of the stored Bell pairs prior to entanglement swapping in presence of their inevitable aging, i.e., decoherence: For a simple instance of a switch with two clients, exponential decay of entanglement fidelity, and a well-known probabilistic but heralded two-to-one distillation protocol, given a threshold end-to-end entanglement fidelity, we use the Markov Decision Processes framework to identify the optimal action policy - to wait, to distill, or to swap that maximizes throughput. We compare the switch's performance under the optimal distillation-enabled policy with that excluding distillation. Simulations of the two policies demonstrate the improvements that are possible in principle via optimal use of distillation with respect to average throughput, average fidelity, and jitter of end-to-end entanglement, as functions of fidelity threshold. Our model thus helps capture the role of entanglement distillation in mitigating the effects of decoherence in a quantum switch in an entanglement distribution network, adding to the growing literature on quantum switches.

15.Enhanced optomechanical interaction in the unbalanced interferometer

Authors:Alexandr Karpenko Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia, Mikhail Korobko Institut fur Laserphysik, Zentrum fur Optische Quantentechnologien, Universitat Hamburg, Hamburg, Germany, Sergey P. Vyatchanin Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia Quantum Technology Centre, M.V. Lomonosov Moscow State University, Moscow, Russia

Abstract: Quantum optomechanical systems enable the study of fundamental questions on quantum nature of massive objects. For that a strong coupling between light and mechanical motion is required, which presents a challenge for massive objects. In particular large interferometric sensors with low frequency oscillators are difficult to bring into quantum regime. Here we propose a modification of the Michelson-Sagnac interferometer, which allows to boost the optomechanical coupling strength. This is done by unbalancing the central beam-splitter of the interferometer, allowing to balance two types of optomechanical coupling present in the system: dissipative and dispersive. We analyse two different configurations, when the optomechanical cavity is formed by the mirror for the laser pump field (power-recycling), and by the mirror for the signal field (signal-recycling). We show that the imbalance of the beam splitter allows to dramatically increase the optical cooling of the test mass motion. We also formulate the conditions for observing quantum radiation-pressure noise and ponderomotive squeezing. Our configuration can serve as the basis for more complex modifications of the interferometer that would utilize the enhanced coupling strength. This will allow to efficiently reach quantum state of large test masses, opening the way to studying fundamental aspects of quantum mechanics and experimental search for quantum gravity.

16.Direct observation of non-linear optical phase shift induced by a single quantum emitter in a waveguide

Authors:Mathias J. R. Staunstrup, Alexey Tiranov, Ying Wang, Sven Scholz, Andreas D. Wieck, Arne Ludwig, Leonardo Midolo, Nir Rotenberg, Peter Lodahl, Hanna Le Jeannic

Abstract: Realizing a sensitive photon-number-dependent phase shift on a light beam is required both in classical and quantum photonics. It may lead to new applications for classical and quantum photonics machine learning or pave the way for realizing photon-photon gate operations. Non-linear phase-shifts require efficient light-matter interaction, and recently quantum dots coupled to nanophotonic devices have enabled near-deterministic single-photon coupling. We experimentally realize an optical phase shift of $0.19 \pi \pm 0.03$ radians ($\approx 34$ degrees) using a weak coherent state interacting with a single quantum dot in a planar nanophotonic waveguide. The phase shift is probed by interferometric measurements of the light scattered from the quantum dot in the waveguide. The nonlinear process is sensitive at the single-photon level and can be made compatible with scalable photonic integrated circuitry. The work may open new prospects for realizing high-efficiency optical switching or be applied for proof-of-concept quantum machine learning or quantum simulation demonstrations.

17.Recovering quantum entanglement after its certification

Authors:Hyeon-Jin Kim, Ji-Hyeok Jung, Kyung-Jun Lee, Young-Sik Ra

Abstract: Entanglement is a crucial quantum resource with broad applications in quantum information science. For harnessing entanglement in practice, it is a prerequisite to certify the entanglement of a given quantum state. However, the certification process itself destroys the entanglement, thereby precluding further exploitation of the entanglement. Resolving this conflict, here we present a protocol that certifies the entanglement of a quantum state without complete destruction, and then, probabilistically recovers the original entanglement to provide useful entanglement for further quantum applications. We experimentally demonstrate this protocol in a photonic quantum system, and highlight its usefulness for selecting high-quality entanglement from a realistic entanglement source. Moreover, our study reveals various tradeoff relations among the physical quantities involved in the protocol. Our results show how entanglement certification can be made compatible with subsequent quantum applications, and more importantly, be beneficial to sort entanglement for better performance in quantum technologies.

18.Entropy Constraints for Ground Energy Optimization

Authors:Hamza Fawzi, Omar Fawzi, Samuel O. Scalet

Abstract: We study the use of von Neumann entropy constraints for obtaining lower bounds on the ground energy of quantum many-body systems. Known methods for obtaining certificates on the ground energy typically use consistency of local observables and are expressed as semidefinite programming relaxations. The local marginals defined by such a relaxation do not necessarily satisfy entropy inequalities that follow from the existence of a global state. Here, we propose to add such entropy constraints that lead to tighter convex relaxations for the ground energy problem. We give analytical and numerical results illustrating the advantages of such entropy constraints. We also show limitations of the entropy constraints we construct: they are implied by doubling the number of sites in the relaxation and as a result they can at best lead to a quadratic improvement in terms of the matrix sizes of the variables. We explain the relation to a method for approximating the free energy known as the Markov Entropy Decomposition method.

19.Why Bohr was wrong in his response to EPR

Authors:Aurélien Drezet

Abstract: We assess the analysis made by Bohr in 1935 of the Einstein Podolsky Rosen paradox/theorem. We explicitly describe Bohr's gedanken experiment involving a double-slit moving diaphragm interacting with two independent particles and show that the analysis provided by Bohr was flawed. We propose a different protocol correcting Bohr's version that confirms EPR dilemma: Quantum mechanics is either incomplete or non-local.

20.Unified direct parameter estimation via quantum reservoirs

Authors:Yinfei Li, Sanjib Ghosh, Jiangwei Shang, Qihua Xiong, Xiangdong Zhang

Abstract: Parameter estimation is an indispensable task in various applications of quantum information processing. To predict parameters in the post-processing stage, it is inherent to first perceive the quantum state with a measurement protocol and store the information acquired. In this work, we propose a general framework for constructing classical approximations of arbitrary quantum states with quantum reservoir networks. A key advantage of our method is that only a single local measurement setting is required for estimating arbitrary parameters, while most of the previous methods need exponentially increasing number of measurement settings. To estimate $M$ parameters simultaneously, the size of the classical approximation scales as $\ln M$. Moreover, this estimation scheme is extendable to higher-dimensional as well as hybrid systems, which makes it exceptionally generic. Both linear and nonlinear functions can be estimated efficiently by our scheme, and we support our theoretical findings with extensive numerical simulations.

21.Abelian and non-abelian quantum two-block codes

Authors:Renyu Wang, Hsiang-Ku Lin, Leonid P. Pryadko

Abstract: We discuss quantum two-block codes, a large class of CSS codes constructed from two commuting square matrices.Interesting families of such codes are generalized-bicycle (GB) codes and two-block group-algebra (2BGA) codes, where a cyclic group is replaced with an arbitrary finite group, generally non-abelian. We present code construction and give several expressions for code dimension, applicable depending on whether the constituent group is cyclic, abelian, or non-abelian. This gives a simple criterion for an essentially non-abelian 2BGA code guaranteed not to be permutation-equivalent to such a code based on an abelian group. We also give a lower bound on the distance which, in particular, applies to the case when a 2BGA code reduces to a hypergraph-product code constructed from a pair of classical group codes.

22.Adaptive variational simulation for open quantum systems

Authors:Huo Chen, Niladri Gomes, Siyuan Niu, Wibe Albert de Jong

Abstract: Emerging quantum hardware provides new possibilities for quantum simulation. While much of the research has focused on simulating closed quantum systems, the real-world quantum systems are mostly open. Therefore, it is essential to develop quantum algorithms that can effectively simulate open quantum systems. Here we present an adaptive variational quantum algorithm for simulating open quantum system dynamics described by the Lindblad equation. The algorithm is designed to build resource-efficient ansatze through the dynamical addition of operators by maintaining the simulation accuracy. We validate the effectiveness of our algorithm on both noiseless simulators and IBM quantum processors and observe good quantitative and qualitative agreement with the exact solution. We also investigate the scaling of the required resources with system size and accuracy and find polynomial behavior. Our results demonstrate that near-future quantum processors are capable of simulating open quantum systems.

23.Fault-tolerant quantum algorithm for symmetry-adapted perturbation theory

Authors:Cristian L. Cortes, Matthias Loipersberger, Robert M. Parrish, Sam Morley-Short, William Pol, Sukin Sim, Mark Steudtner, Christofer S. Tautermann, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, Michael Streif

Abstract: The efficient computation of observables beyond the total energy is a key challenge and opportunity for fault-tolerant quantum computing approaches in quantum chemistry. Here we consider the symmetry-adapted perturbation theory (SAPT) components of the interaction energy as a prototypical example of such an observable. We provide a guide for calculating this observable on a fault-tolerant quantum computer while optimizing the required computational resources. Specifically, we present a quantum algorithm that estimates interaction energies at the first-order SAPT level with a Heisenberg-limited scaling. To this end, we exploit a high-order tensor factorization and block encoding technique that efficiently represents each SAPT observable. To quantify the computational cost of our methodology, we provide resource estimates in terms of the required number of logical qubits and Toffoli gates to execute our algorithm for a range of benchmark molecules, also taking into account the cost of the eigenstate preparation and the cost of block encoding the SAPT observables. Finally, we perform the resource estimation for a heme and artemisinin complex as a representative large-scale system encountered in drug design, highlighting our algorithm's performance in this new benchmark study and discussing possible bottlenecks that may be improved in future work.

24.A Nonadditive Quantum Code with Exotic Transversal Gate Set

Authors:Eric Kubischta, Ian Teixeira

Abstract: We exhibit a $ ((7,2,3)) $ nonadditive quantum error correcting code whose single qubit transversal gate set is $2I$, the binary icosahedral group. No code has ever been demonstrated with this property. The group $2I$ has intrinsic interest as a maximal subgroup of $SU(2)$. But more importantly, $ 2I $ together with a certain involution forms the most efficient single-qubit universal gate set.

25.2D Hamiltonians with exotic bipartite and topological entanglement

Authors:Shankar Balasubramanian, Ethan Lake, Soonwon Choi

Abstract: We present a class of exactly solvable 2D models whose ground states violate conventional beliefs about entanglement scaling in quantum matter. These beliefs are (i) that area law entanglement scaling originates from local correlations proximate to the boundary of the entanglement cut, and (ii) that ground state entanglement in 2D Hamiltonians cannot violate area law scaling by more than a multiplicative logarithmic factor. We explicitly present two classes of models defined by local, translation-invariant Hamiltonians, whose ground states can be exactly written as weighted superpositions of framed loop configurations. The first class of models exhibits area-law scaling, but of an intrinsically nonlocal origin so that the topological entanglement entropy scales with subsystem sizes. The second class of models has a rich ground state phase diagram that includes a phase exhibiting volume law entanglement.

1.A round-trip multi-band quantum access network

Authors:Yuehan Xu, Tao Wang, Huanxi Zhao, Peng Huang, Guihua Zeng

Abstract: The quantum network makes use of the quantum states to transmit data, which will revolutionize classical communication and allow for some breakthrough applications. The quantum key distribution (QKD) is one prominent application of quantum networks, and can protect the data transmission through quantum mechanics. In this work, we propose an expandable and cost-effective quantum access network, in which the round-trip structure makes quantum states travel in a circle to carry the information, and the multi-band technique is proposed to support multi-user access. Based on the round-trip multi-band quantum access network, we realize multi-user secure key sharing through the continuous-variable QKD (CV-QKD) protocol. Due to the encoding characteristics of CV-QKD, the quadrature components in different frequency bands can be used to transmit key information for different users. The feasibility of this scheme is confirmed by comprehensive noise analysis, and is verified by a proof-of-principle experiment. The results show that each user can achieve excess noise suppression and 600 bps level secure key generation under 30 km standard fiber transmission. Such networks have the ability of multi-user access theoretically and could be expanded by plugging in simple modules. Therefore, it paves the way for near-term large-scale quantum secure networks.

2.A security framework for quantum key distribution implementations

Authors:Guillermo Currás-Lorenzo, Margarida Pereira, Go Kato, Marcos Curty, Kiyoshi Tamaki

Abstract: Quantum key distribution (QKD) can theoretically achieve the Holy Grail of cryptography, information-theoretic security against eavesdropping. However, in practice, discrepancies between the mathematical models assumed in security proofs and the actual functioning of the devices used in implementations prevent it from reaching this goal. Since measurement-device-independent QKD guarantees security with arbitrarily flawed receivers, the missing step is securing the sources. So far, all efforts in this regard have come at a price; some proofs are suitable only for particular source imperfections, while others severely compromise the system's performance, i.e., its communication speed and distance. Meanwhile, device-independent QKD is far from being a satisfactory solution, as it is vulnerable to memory attacks, it cannot incorporate information leakage from the user devices in a device-independent manner, and its performance is poor. Here, we solve this crucial problem by presenting a security proof that is robust against all practical source imperfections while maintaining high performance. Moreover, our proof requires minimal state characterization, which facilitates its application to real-life implementations. We anticipate that, thanks to these advantages, it will serve as a basis for the standardization of QKD sources.

3.Novel Quantum Information Processing Methods and Investigation

Authors:Zhang Ze Yu

Abstract: Quantum information processing and its subfield, quantum image processing, are rapidly growing fields as a result of advancements in the practicality of quantum mechanics. In this paper, we propose a quantum algorithm for processing information, such as one-dimensional time series and two-dimensional images, in the frequency domain. The information of interest is encoded into the magnitude of probability amplitude or the coefficient of each basis state. The oracle for filtering operates based on postselection results, and its explicit circuit design is presented. This oracle is versatile enough to perform all basic filtering, including high pass, low pass, band pass, band stop, and many other processing techniques. Finally, we present two novel schemes for transposing matrices in this paper. They use similar encoding rules but with deliberate choices in terms of selecting basis states. These schemes could potentially be useful for other quantum information processing tasks, such as edge detection. The proposed techniques are implemented on the IBM Qiskit quantum simulator. Some results are compared with traditional information processing results to verify their correctness and are presented in this paper.

4.Private Product Computation using Quantum Entanglement

Authors:René Bødker Christensen, Petar Popovski

Abstract: In this work, we show that a pair of entangled qubits can be used to compute a product privately. More precisely, two participants with a private input from a finite field can perform local operations on a shared, Bell-like quantum state, and when these qubits are later sent to a third participant, the third participant can determine the product of the inputs, but without learning more about the individual inputs. We give a concrete way to realize this product computation for arbitrary finite fields of prime order.

5.A thermodynamic approach to optimization in complex quantum systems

Authors:Alberto Imparato, Nicholas Chancellor, Gabriele De Chiara

Abstract: We consider the problem of finding the energy minimum of a complex quantum Hamiltonian by employing a non-Markovian bath prepared in a low energy state. The energy minimization problem is thus turned into a thermodynamic cooling protocol in which we repeatedly put the system of interest in contact with a colder auxiliary system. By tuning the internal parameters of the bath, we show that the optimal cooling is obtained in a regime where the bath exhibits a quantum phase transition in the thermodynamic limit. This result highlights the importance of collective effects in thermodynamic devices. We furthermore introduce a two-step protocol that combines the interaction with the bath with a measure of its energy. While this protocol does not destroy coherence in the system of interest, we show that it can further enhance the cooling effect.

6.Scaling of entangling-gate errors in large ion crystals

Authors:Wenhao He, Wenhao Zhang, Xiao Yuan, Yangchao Shen, Xiao-Ming Zhang

Abstract: Trapped-ion has shown great advantages in building quantum computers. While high fidelity entangling-gate has been realized for few ions, how to maintain the high fidelity for large scale trapped-ions still remains an open problem.Here, we present an analysis on arbitrary scale ion chain and focus on motional-related errors, reported as one of the leading error sources in state-of-the-art experiments. We theoretically analyze two-qubit entangling-gate infidelity in a large ion crystal. To verify our result, we develop an efficient numerical simulation algorithm that avoids exponential increases of the Hilbert space dimension. For the motional heating error, We derive a much tighter bound of gate infidelity than previously estimated $O(N\Gamma\tau)$, and we give an intuitive understanding from the trajectories in the phase space of motional modes. Our discoveries may inspire the scheme of pulse design against incoherent errors and shed light on the way toward constructing scalable quantum computers with large ion crystals.

7.Interpretation of the superposition principle and locality loophole in Bell experiments

Authors:Sheng Feng

Abstract: A connection is revealed between the superposition principle and locality. A self consistent interpretation of the superposition principle is put forth, from which it is shown that quantum mechanics may be a local statistical theory. Then it is shown how Bell experiments can be satisfactorily explained by assuming local nature for entangled particles, i.e., the violation of Bell inequality cannot distinguish between locality and nonlocality, which is referred to as locality loophole. Moreover, existing experimental results are presented indicating locality in quantum mechanics and new experiments are proposed so that the locality loophole may be closed.

8.A New Quantum Advantage in Quantum Secret Sharing

Authors:Pahulpreet Singh, Indranil Chakrabarty

Abstract: In this letter, we consider a simple three-party scenario, with one Dealer (Alice), one Assistant (Bob) and a Reconstructor (Charlie). We find the classical limit of reconstructing the quantum secret under this framework. Interestingly this happens to be 2/3. We formulate the expression for reconstruction fidelity in terms of the Bloch parameters of the shared resource state. It is imperative to say at this point any resource state for which the score is beyond 2/3, gives us a quantum advantage in context of reconstructing the secret. Interestingly, this fidelity not only depends upon the tripartite correlation tensor but also on the existent bipartite channel between the dealer and the reconstructor. This fidelity in a sense is able to measure, the amount of information we are able to reconstruct. As a result of which it also takes into account the contribution of the teleportation capacity of the channel between the dealer and reconstructor in addition to the secret sharing capacity of three qubit resource state. In this work along with example we also discuss the cases when the quantum advantage in the reconstruction fidelity is entirely because of the secret sharing process (where involvement of three party is necessary) or entirely because of the teleportation in subsystem or because of. We are able to show quantum advantages in all possible scenarios with states other than the standard GHZ state. We also obtain necessary conditions based on the correlation tensor between three parties and correlation matrix between the dealer and the reconstructor. In this letter we discover a new kind of interoperability that happens in the process of secret sharing and teleportation for a given tripartite resource. This result benchmarks the identification process of three qubit resources for these tasks while setting up large scale quantum network.

9.Enhancing Quantum Support Vector Machines through Variational Kernel Training

Authors:Nouhaila Innan, Muhammed Al-Zafar Khan, Biswaranjan Panda, Mohamed Bennai

Abstract: Quantum machine learning (QML) has witnessed immense progress recently, with quantum support vector machines (QSVMs) emerging as a promising model. This paper focuses on the two existing QSVM methods: quantum kernel SVM (QK-SVM) and quantum variational SVM (QV-SVM). While both have yielded impressive results, we present a novel approach that synergizes the strengths of QK-SVM and QV-SVM to enhance accuracy. Our proposed model, quantum variational kernel SVM (QVK-SVM), leverages the quantum kernel and quantum variational algorithm. We conducted extensive experiments on the Iris dataset and observed that QVK-SVM outperforms both existing models in terms of accuracy, loss, and confusion matrix indicators. Our results demonstrate that QVK-SVM holds tremendous potential as a reliable and transformative tool for QML applications. Hence, we recommend its adoption in future QML research endeavors.

10.Exact solution for the time-dependent quantum oscillator

Authors:E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva, A. A. Korepanova

Abstract: In this paper, an exact solution of the Schr\"odinger equation for the time-dependent potential $U\left( x,t \right)={m\,{{\Omega }^{2}}\left( t \right){{x}^{2}}}/{2}\;$ is constructed, where the frequency $\Omega \left( t \right)$ is a "sufficiently" smooth function of time. For the quantum system under consideration, a set of wave functions and a spectrum of time-dependent energy eigenvalues are obtained. The behavior of the time-dependent potential affects the instability of the quantum system. The dynamics of the system is described by the Hill equation. The time-dependent Wigner function and its generalization to the phase space of higher kinematic values are found in an explicit form. The process of energy "pumping" of a quantum system, which leads to its instability, is considered in detail.

11.Continuous dynamical decoupling of optical $^{171}$Yb$^{+}$ qudits with radiofrequency fields

Authors:Ilia V. Zalivako, Alexander S. Borisenko, Ilya A. Semerikov, Andrey Korolkov, Pavel L. Sidorov, Kristina Galstyan, Nikita V. Semenin, Vasiliy Smirnov, Mikhail A. Aksenov, Aleksey K. Fedorov, Ksenia Yu. Khabarova, Nikolay N. Kolachevsky

Abstract: The use of multilevel quantum information carriers, also known as qudits, attracts a significant deal of interest as a way for further scalability of quantum computing devices. However, a nontrivial task is to experimentally achieve a gain in the efficiency of realizing quantum algorithms with qudits since higher qudit levels typically have relatively short coherence times compared to qubit states. Here we propose and experimentally demonstrate two approaches for the realization of continuous dynamical decoupling of magnetic-sensitive states with $m_F=\pm1$ for qudits encoded in optical transition of trapped $^{171}$Yb$^{+}$ ions. We achieve improvement in qudit levels coherence time by the order of magnitude (more than 9 ms) without any magnetic shielding, which reveals the potential advantage of the symmetry of the $^{171}$Yb$^{+}$ ion energy structure for counteracting the magnetic field noise. Our results are a step towards the realization of qudit-based algorithms using trapped ions.

12.Complete complementarity relations for three-flavor neutrino oscillations

Authors:Massimo Blasone, Silvio De Siena, Cristina Matrella

Abstract: We exploit complete complementarity relations to characterize quantum correlations encoded in a three-flavor oscillating neutrino system. In particular, we analyze the contributions associated to the twoflavor subsystems, each of which exhibits a particular internal structure. We focus on the behavior of the correlations at large distances, both for an initial electron and muon neutrino state. Our analysis is based on the wave packet approach in which the neutrino is represented by a mixed state: consequently, the bipartite correlations are described by the Quantum Discord.

13.One-Way Deficit and Holevo Quantity of Generalized $n$-qubit Werner State

Authors:Yao-Kun Wang, Rui-Xin Chen, Li-Zhu Ge, Shao-Ming Fei, Zhi-Xi Wang

Abstract: Originated from the work extraction in quantum systems coupled to a heat bath, quantum deficit is a kind of significant quantum correlations like quantum entanglement. It links quantum thermodynamics with quantum information. We analytically calculate the one-way deficit of the generalized $n$-qubit Werner state. We find that the one-way deficit increases as the mixing probability $p$ increases for any $n$. For fixed $p$, we observe that the one-way deficit increases as $n$ increases. For any $n$, the maximum of one-way deficit is attained at $p=1$. Furthermore, for large $n$ ($2^n \rightarrow \infty$), we prove that the curve of one-way deficit versus $p$ approaches to a straight line with slope $1$. We also calculate the Holevo quantity for the generalized $n$-qubit Werner state, and show that it is zero.

14.Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model

Authors:Pablo Viñas Martínez, Esperanza López Manzanares, Alejandro Bermudez Carballo

Abstract: The quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins, which are encoded in the internal electronic states of the ions, and measured in experiments that probe the real-time dynamics. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field $\phi(x)$ locally coupled to the spins that acts as a carrier, leading to an analogue of pion-mediated Yukawa interactions. In the vicinity of a structural transition of the ion crystal, one must go beyond the Klein-Gordon fields, and include additional $\lambda\phi^4$ terms responsible for phonon-phonon scattering. This leads to quantum effects that can be expressed by Feynman loop integrals that modify the range of the Yukawa-type spin interactions; an effect that could be used to probe the underlying fixed point of this quantum field theory (QFT). Unfortunately, the rigidity of the trapped-ion crystal makes it challenging to observe genuine quantum effects, such as the flow of the critical point with the quartic coupling $\lambda$. We hereby show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs. We perform self-consistent calculations that resum certain Feynman diagrams and, additionally, go beyond mean-field theory to predict how measurements on the trapped-ion spin system can probe key properties of the $\lambda\phi^4$ QFT.

15.Sensitive AC and DC Magnetometry with Nitrogen-Vacancy Center Ensembles in Diamond

Authors:John F. Barry, Matthew H. Steinecker, Scott T. Alsid, Jonah Majumder, Linh M. Pham, Michael F. O'Keefe, Danielle A. Braje

Abstract: Quantum sensing with solid-state spins offers the promise of high spatial resolution, bandwidth, and dynamic range at sensitivities comparable to more mature quantum sensing technologies, such as atomic vapor cells and superconducting devices. However, despite comparable theoretical sensitivity limits, the performance of bulk solid-state quantum sensors has so far lagged behind these more mature alternatives. A recent review~\cite{barry2020sensitivity} suggests several paths to improve performance of magnetometers employing nitrogen-vacancy defects in diamond, the most-studied solid-state quantum sensing platform. Implementing several suggested techniques, we demonstrate the most sensitive nitrogen-vacancy-based bulk magnetometer reported to date. Our approach combines tailored diamond growth to achieve low strain and long intrinsic dephasing times, the use of double-quantum Ramsey and Hahn echo magnetometry sequences for broadband and narrowband magnetometry respectively, and P1 driving to further extend dephasing time. Notably, the device does not include a flux concentrator, preserving the fixed response of the NVs to magnetic field. The magnetometer realizes a broadband \textcolor{mhsnew}{near-}DC sensitivity $\sim 460$~fT$\cdot$s$^{1/2}$ and a narrowband AC sensitivity $\sim 210$~fT$\cdot$s$^{1/2}$. We describe the experimental setup in detail and highlight potential paths for future improvement.

16.Unitary equivalence of the twisted quantum states

Authors:N. V. Filina, S. S. Baturin

Abstract: We study the time dynamics of the twisted quantum states. We find an explicit connection between the well-known stationary Landau state and an evolving twisted state, even if the Hamiltonian accounts for the linear energy dissipation. Utilizing this unitary connection, we analyze nonstationary Landau states and unveil some of their properties. We demonstrate how the proposed transformation enables simple evaluation of the different operator mean values for the evolving twisted state based on the solution to the classical Ermakov equation and matrix elements calculated on the stationary Landau states. We anticipate that suggested formalism may significantly simplify the analysis and become a convenient tool for the further theoretical development of the dissipative evolution of the twisted quantum wave packet.

1.Architectural Vision for Quantum Computing in the Edge-Cloud Continuum

Authors:Alireza Furutanpey, Johanna Barzen, Marvin Bechtold, Schahram Dustdar, Frank Leymann, Philipp Raith, Felix Truger

Abstract: Quantum processing units (QPUs) are currently exclusively available from cloud vendors. However, with recent advancements, hosting QPUs is soon possible everywhere. Existing work has yet to draw from research in edge computing to explore systems exploiting mobile QPUs, or how hybrid applications can benefit from distributed heterogeneous resources. Hence, this work presents an architecture for Quantum Computing in the edge-cloud continuum. We discuss the necessity, challenges, and solution approaches for extending existing work on classical edge computing to integrate QPUs. We describe how warm-starting allows defining workflows that exploit the hierarchical resources spread across the continuum. Then, we introduce a distributed inference engine with hybrid classical-quantum neural networks (QNNs) to aid system designers in accommodating applications with complex requirements that incur the highest degree of heterogeneity. We propose solutions focusing on classical layer partitioning and quantum circuit cutting to demonstrate the potential of utilizing classical and quantum computation across the continuum. To evaluate the importance and feasibility of our vision, we provide a proof of concept that exemplifies how extending a classical partition method to integrate quantum circuits can improve the solution quality. Specifically, we implement a split neural network with optional hybrid QNN predictors. Our results show that extending classical methods with QNNs is viable and promising for future work.

2.A Scalable Evaluation of Integer Factorization Performance on IBM Quantum Simulator

Authors:Junseo Lee, Kibum Bae, Chang-Nyoung Song, Hyunchul Jung

Abstract: With the development of quantum technologies, the performance of quantum computing simulators continues to be matured. Given the potential threat of quantum computing to cyber security, it is required to assess the possibility in practice from a current point of view. In this research, we scalably measure the integer factorization time using Shor's algorithm given numerous numbers in the gate-based quantum computing simulator, simulator\_mps. Also, we show the impact of the pre-selection of Shor's algorithm. Specifically, the pre-selection ensures the success rate of integer factorization with a reduced number of iterations, thereby enabling performance measurement under fixed conditions. The comparative result against the random selection of a parameter shows that the pre-selection of a parameter enables scalable evaluation of integer factorization with high efficiency.

3.Two-qubit operations for finite-energy Gottesman-Kitaev-Preskill encodings

Authors:Ivan Rojkov, Paul Moser Röggla, Martin Wagener, Moritz Fontboté-Schmidt, Stephan Welte, Jonathan Home, Florentin Reiter

Abstract: We present techniques for performing two-qubit gates on Gottesman-Kitaev-Preskill (GKP) codes with finite energy, and find that operations designed for ideal infinite-energy codes create undesired entanglement when applied to physically realistic states. We demonstrate that this can be mitigated using recently developed local error-correction protocols, and evaluate the resulting performance. We also propose energy-conserving finite-energy gate implementations which largely avoid the need for further correction.

4.Analytically Solvable Model for Qubit-Mediated Energy Transfer between Quantum Batteries

Authors:Alba Crescente, Dario Ferraro, Matteo Carrega, Maura Sassetti

Abstract: The coherent energy transfer between two identical two-level systems is investigated. Here, the first quantum system plays the role of a charger, while the second can be seen as a quantum battery. Firstly, a direct energy transfer between the two objects is considered and then compared to a transfer mediated by an additional intermediate two-level system. In this latter case, it is possible to distinguish between a two-step process, where the energy is firstly transferred from the charger to the mediator and only after from the mediator to the battery, and a single-step in which the two transfers occurs simultaneously. The differences between these configurations are discussed in the framework of an analytically solvable model completing what recently discussed in literature.

5.On the Bell Experiment and Quantum Foundation

Authors:Inge S. Helland

Abstract: The Bell experiment is discussed in light of a new approach towards the foundation of quantum mechanics. It is concluded from the basic model that the mind of any observer must be limited in some way: In certain contexts, he is simply not able to keep enough variables in his mind when making decisions. This has consequences for Bell's theorem, but it also seems to have wider consequences.

6.Experimentally demonstrating indefinite causal order algorithms to solve the generalized Deutsch's problem

Authors:Wen-Qiang Liu, Zhe Meng, Bo-Wen Song, Jian Li, Qing-Yuan Wu, Xiao-Xiao Chen, Jin-Yang Hong, An-Ning Zhang, Zhang-qi Yin

Abstract: Deutsch's algorithm is the first quantum algorithm to show the advantage over the classical algorithm. Here we generalize Deutsch's problem to $n$ functions and propose a new quantum algorithm with indefinite causal order to solve this problem. The new algorithm not only reduces the number of queries to the black-box by half over the classical algorithm, but also significantly reduces the number of required quantum gates over the Deutsch's algorithm. We experimentally demonstrate the algorithm in a stable Sagnac loop interferometer with common path, which overcomes the obstacles of both phase instability and low fidelity of Mach-Zehnder interferometer. The experimental results have shown both an ultra-high and robust success probability $\sim 99.7\%$. Our work opens up a new path towards solving the practical problems with indefinite casual order quantum circuits.

7.Attention-Based Transformer Networks for Quantum State Tomography

Authors:Hailan Ma, Zhenhong Sun, Daoyi Dong, Chunlin Chen, Herschel Rabitz

Abstract: Neural networks have been actively explored for quantum state tomography (QST) due to their favorable expressibility. To further enhance the efficiency of reconstructing quantum states, we explore the similarity between language modeling and quantum state tomography and propose an attention-based QST method that utilizes the Transformer network to capture the correlations between measured results from different measurements. Our method directly retrieves the density matrices of quantum states from measured statistics, with the assistance of an integrated loss function that helps minimize the difference between the actual states and the retrieved states. Then, we systematically trace different impacts within a bag of common training strategies involving various parameter adjustments on the attention-based QST method. Combining these techniques, we establish a robust baseline that can efficiently reconstruct pure and mixed quantum states. Furthermore, by comparing the performance of three popular neural network architectures (FCNs, CNNs, and Transformer), we demonstrate the remarkable expressiveness of attention in learning density matrices from measured statistics.

8.Toward universal transformations of orbital angular momentum of a single photon

Authors:Dong-Xu Chen, Yunlong Wang, Feiran Wang, Jun-Long Zhao, Chui-Ping Yang

Abstract: High-dimensional quantum systems offer many advantages over low-dimensional quantum systems. Meanwhile, unitary transformations on quantum states are important parts in various quantum information tasks, whereas they become technically infeasible as the dimensionality increases. The photonic orbital angular momentum (OAM), which is inherit in the transverse spatial mode of photons, offers a natural carrier to encode information in high-dimensional spaces. However, it's even more challenging to realize arbitrary unitary transformations on the photonic OAM states. Here, by combining the path and OAM degrees of freedom of a single photon, an efficient scheme to realize arbitrary unitary transformations on the path-OAM coupled quantum states is proposed. The proposal reduces the number of required interferometers by approximately one quarter compared with previous works, while maintaining the symmetric structure. It is shown that by using OAM-to-path interfaces, this scheme can be utilized to realize arbitrary unitary transformations on the OAM states of photons. This work facilitates the development of high-dimension quantum state transformations, and opens a new door to the manipulation of the photonic OAM states.

9.Entanglement-Assisted Covert Communication via Qubit Depolarizing Channels

Authors:Elyakim Zlotnick, Boulat Bash, Uzi Pereg

Abstract: We consider entanglement-assisted communication over the qubit depolarizing channel under the security requirement of covert communication, where not only the information is kept secret, but the transmission itself must be concealed from detection by an adversary. Previous work showed that $O(\sqrt{n})$ information bits can be reliably and covertly transmitted in $n$ channel uses without entanglement assistance. However, Gagatsos et al. (2020) showed that entanglement assistance can increase this scaling to $O(\sqrt{n}\log(n))$ for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that $O(\sqrt{n}\log(n))$ covert bits can be transmitted reliably over $n$ uses of a qubit depolarizing channel.

10.High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit

Authors:Shuo Ma, Genyue Liu, Pai Peng, Bichen Zhang, Sven Jandura, Jahan Claes, Alex P. Burgers, Guido Pupillo, Shruti Puri, Jeff D. Thompson

Abstract: The development of scalable, high-fidelity qubits is a key challenge in quantum information science. Neutral atom qubits have progressed rapidly in recent years, demonstrating programmable processors and quantum simulators with scaling to hundreds of atoms. Exploring new atomic species, such as alkaline earth atoms, or combining multiple species can provide new paths to improving coherence, control and scalability. For example, for eventual application in quantum error correction, it is advantageous to realize qubits with structured error models, such as biased Pauli errors or conversion of errors into detectable erasures. In this work, we demonstrate a new neutral atom qubit, using the nuclear spin of a long-lived metastable state in ${}^{171}$Yb. The long coherence time and fast excitation to the Rydberg state allow one- and two-qubit gates with fidelities of 0.9990(1) and 0.980(1), respectively. Importantly, a significant fraction of all gate errors result in decays out of the qubit subspace, to the ground state. By performing fast, mid-circuit detection of these errors, we convert them into erasure errors; during detection, the induced error probability on qubits remaining in the computational space is less than $10^{-5}$. This work establishes metastable ${}^{171}$Yb as a promising platform for realizing fault-tolerant quantum computing.

11.Fast analytic and numerical design of superconducting resonators in flip-chip architectures

Authors:Hang-Xi Li, Daryoush Shiri, Sandoko Kosen, Marcus Rommel, Lert Chayanun, Andreas Nylander, Robert Rehammer, Giovanna Tancredi, Marco Caputo, Kestutis Grigoras, Leif Grönberg, Joonas Govenius, Jonas Bylander

Abstract: In superconducting quantum processors, the predictability of device parameters is of increasing importance as many labs scale up their systems to larger sizes in a 3D-integrated architecture. In particular, the properties of superconducting resonators must be controlled well to ensure high-fidelity multiplexed readout of qubits. Here we present a method, based on conformal mapping techniques, to predict a resonator's parameters directly from its 2D cross-section, without computationally heavy simulation. We demonstrate the method's validity by comparing the calculated resonator frequency and coupling quality factor with those obtained through 3D finite-element-method simulation and by measurement of 15 resonators in a flip-chip-integrated architecture. We achieve a discrepancy of less than 2% between designed and measured frequencies, for 6-GHz resonators. We also propose a design method that reduces the sensitivity of the resonant frequency to variations in the inter-chip spacing.

12.Quantum Approximate Optimization Algorithm with Cat Qubits

Authors:Pontus Vikstål, Laura García-Álvarez, Shruti Puri, Giulia Ferrini

Abstract: The Quantum Approximate Optimization Algorithm (QAOA) -- one of the leading algorithms for applications on intermediate-scale quantum processors -- is designed to provide approximate solutions to combinatorial optimization problems with shallow quantum circuits. Here, we study QAOA implementations with cat qubits, using coherent states with opposite amplitudes. The dominant noise mechanism, i.e., photon losses, results in $Z$-biased noise with this encoding. We consider in particular an implementation with Kerr resonators. We numerically simulate solving MaxCut problems using QAOA with cat qubits by simulating the required gates sequence acting on the Kerr non-linear resonators, and compare to the case of standard qubits, encoded in ideal two-level systems, in the presence of single-photon loss. Our results show that running QAOA with cat qubits increases the approximation ratio for random instances of MaxCut with respect to qubits encoded into two-level systems.

13.Massively Parallel Tensor Network State Algorithms on Hybrid CPU-GPU Based Architectures

Authors:Andor Menczer, Örs Legeza

Abstract: The interplay of quantum and classical simulation and the delicate divide between them is in the focus of massively parallelized tensor network state (TNS) algorithms designed for high performance computing (HPC). In this contribution, we present novel algorithmic solutions together with implementation details to extend current limits of TNS algorithms on HPC infrastructure building on state-of-the-art hardware and software technologies. Benchmark results obtained via large-scale density matrix renormalization group (DMRG) simulations are presented for selected strongly correlated molecular systems addressing problems on Hilbert space dimensions up to $2.88\times10^{36}$.

14.Pooling techniques in hybrid quantum-classical convolutional neural networks

Authors:Maureen Monnet, Hanady Gebran, Andrea Matic-Flierl, Florian Kiwit, Balthasar Schachtner, Amine Bentellis, Jeanette Miriam Lorenz

Abstract: Quantum machine learning has received significant interest in recent years, with theoretical studies showing that quantum variants of classical machine learning algorithms can provide good generalization from small training data sizes. However, there are notably no strong theoretical insights about what makes a quantum circuit design better than another, and comparative studies between quantum equivalents have not been done for every type of classical layers or techniques crucial for classical machine learning. Particularly, the pooling layer within convolutional neural networks is a fundamental operation left to explore. Pooling mechanisms significantly improve the performance of classical machine learning algorithms by playing a key role in reducing input dimensionality and extracting clean features from the input data. In this work, an in-depth study of pooling techniques in hybrid quantum-classical convolutional neural networks (QCCNNs) for classifying 2D medical images is performed. The performance of four different quantum and hybrid pooling techniques is studied: mid-circuit measurements, ancilla qubits with controlled gates, modular quantum pooling blocks and qubit selection with classical postprocessing. We find similar or better performance in comparison to an equivalent classical model and QCCNN without pooling and conclude that it is promising to study architectural choices in QCCNNs in more depth for future applications.

15.Towards Generating Indistinguishable Photons from Solid-State Quantum Emitters at Elevated Temperatures

Authors:Alistair J. Brash, Jake Iles-Smith

Abstract: Indistinguishable photons are a key resource for many optical quantum technologies. Efficient, on-demand single photon sources have been demonstrated using single solid-state quantum emitters, typically epitaxially grown quantum dots in III-V semiconductors. To achieve the highest performance, these sources are typically operated at liquid helium temperatures ($\sim 4~\mathrm{K}$), introducing significant significant size, weight and power (SWAP) considerations that are often impractical for emerging applications such as satelite quantum communications. Here we experimentally verify that coupling a solid-state emitter to a photonic nanocavity can greatly improve photon coherence at higher temperatures where SWAP requirements can be much lower. Using a theoretical model that fully captures the phonon-mediated processes that compromise photon indistinguishability as temperature increases, we reproduce our experimental results and demonstrate the potential to further increase the operating temperature in future generations of optimised devices.

16.Relativistic locality can imply subsystem locality

Authors:Andrea Di Biagio, Richard Howl, Caslav Brukner, Carlo Rovelli, Marios Christodoulou

Abstract: Locality is a central notion in modern physics, but different disciplines understand it in different ways. Quantum field theory focusses on relativistic locality, enforced by microcausality, while quantum information theory focuses on subsystem locality, which regulates how information and causal influences propagate in a system, with no direct reference to spacetime notions. Here we investigate how microcausality and subsystem locality are related. The question is relevant for understanding whether it is possible to formulate quantum field theory in quantum information language, and has bearing on the recent discussions on low-energy tests of quantum gravity. We present a first result in this direction: in the quantum dynamics of a massive scalar quantum field coupled to two localised systems, microcausality implies subsystem locality in a physically relevant approximation.

17.Energy densities in quantum mechanics

Authors:V. Stepanyan, A. E. Allahverdyan

Abstract: Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic description for a spin-$\frac{1}{2}$ particle: Dirac's equation. Employing its energy-momentum tensor and going to the non-relativistic limit we find a locally conserved non-relativistic energy density that is defined via the Terletsky-Margenau-Hill quasiprobability (which is hence selected among other options). It coincides with the weak value of energy, and also with the hydrodynamic energy in the Madelung representation of quantum dynamics, which includes the quantum potential. Moreover, we find a new form of spin-related energy that is finite in the non-relativistic limit, emerges from the rest energy, and is (separately) locally conserved, though it does not contribute to the global energy budget. This form of energy has a holographic character, i.e., its value for a given volume is expressed via the surface of this volume. Our results apply to situations where local energy representation is essential; e.g. we show that the energy transfer velocity of a free Gaussian wave-packet (and also Airy wave-packet) is larger than its group (i.e. coordinate-transfer) velocity.

1.Information capacity analysis of fully correlated multi-level amplitude damping channels

Authors:Rajiuddin Sk, Prasanta K. Panigrahi

Abstract: The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels, which is a challenging task in many instances. Recently, Multi-level Amplitude Damping channel has been introduced, and the corresponding quantum capacity of the channel has been analyzed for a quantum system of dimension d=3 [S. Chessa, V. Giovannetti, Commun. Phys. 4,22 (2021)]. In this paper, we have investigated the information capacity of Multi-level Amplitude Damping Channel for dimension d=3 in presence of correlation between successive applications of the channel. We derive the single-shot classical capacities and quantum capacities associated with a different class of maps for the three-level system. Additionally, we compute the quantum and classical capacities in entanglement-assisted scenarios.

2.The Unified Effect of Data Encoding, Ansatz Expressibility and Entanglement on the Trainability of HQNNs

Authors:Muhammad Kashif, Saif Al-Kuwari

Abstract: In this paper, we propose a framework to study the combined effect of several factors that contribute to the barren plateau problem in quantum neural networks (QNNs), which is a critical challenge in quantum machine learning (QML). These factors include data encoding, qubit entanglement, and ansatz expressibility. To investigate this joint effect in a real-world context, we focus on hybrid quantum neural networks (HQNNs) for multi-class classification. Our proposed framework aims to analyze the impact of these factors on the training landscape of HQNNs. Our findings show that the barren plateau problem in HQNNs is dependent on the expressibility of the underlying ansatz and the type of data encoding. Furthermore, we observe that entanglement also plays a role in the barren plateau problem. By evaluating the performance of HQNNs with various evaluation metrics for classification tasks, we provide recommendations for different constraint scenarios, highlighting the significance of our framework for the practical success of QNNs.

3.From basic science to technological development: the case for two avenues

Authors:Matteo Carlesso, Mauro Paternostro

Abstract: We argue that, in the quest for the translation of fundamental research into actual quantum technologies, two avenues that have - so far - only partly explored should be pursued vigorously. On first entails that the study of energetics at the fundamental quantum level holds the promises for the design of a generation of more energy-efficient quantum devices. On second route to pursue implies a more structural hybridisation of quantum dynamics with data science techniques and tools, for a more powerful framework for quantum information processing.

4.Adaptive Quantum Tomography in a Weak Measurement System with Superconducting Circuits

Authors:Hyeok Hwang, JaeKyung Choi, Eunseong Kim

Abstract: Adaptive tomography has been widely investigated to achieve faster state tomography processing of quantum systems. Infidelity of the nearly pure states in a quantum information process generally scales as O(1/sqrt(N) ), which requires a large number of statistical ensembles in comparison to the infidelity scaling of O(1/N) for mixed states. One previous report optimized the measurement basis in a photonic qubit system, whose state tomography uses projective measurements, to obtain an infidelity scaling of O(1/N). However, this dramatic improvement cannot be applied to weak-value-based measurement systems in which two quantum states cannot be distinguished with perfect measurement fidelity. We introduce in this work a new optimal measurement basis to achieve fast adaptive quantum state tomography and a minimum magnitude of infidelity in a weak measurement system. We expect that the adaptive quantum state tomography protocol can lead to a reduction in the number of required measurements of approximately 33.74% via simulation without changing the O(1/sqrt(N)) scaling. Experimentally, we find a 14.81% measurement number reduction in a superconducting circuit system.

5.Analyzing computational cost of probabilistic imaginary-time evolution method

Authors:Hirofumi Nishi, Koki Hamada, Yusuke Nishiya, Taichi Kosugi, Yu-ichiro Matsushita

Abstract: Ground-state preparation is an important task in quantum computation. The probabilistic imaginary-time evolution (PITE) method is a promising candidate for preparing the ground state of the Hamiltonian, which comprises a single ancilla qubit and forward- and backward-controlled real-time evolution operators. Here, we analyze the computational costs of the PITE method for both linear and exponential scheduling of the imaginary-time step size. First, we analytically discuss an error defined as the closeness between the states acted on by exact and approximate imaginary-time evolution operators. The optimal imaginary-time step size and speed of change of imaginary time were also discussed. Subsequently, the analytical discussion was verified using numerical simulations for a one-dimensional Heisenberg chain. As a result, we conclude that exponential scheduling with slow changes is preferable for reducing the computational costs.

6.Relaxation time as a control parameter for exploring dynamical phase diagrams

Authors:Ángel L. Corps, Pedro Pérez-Fernández, Armando Relaño

Abstract: We explore a full dynamical phase diagram by means of a double quench protocol that depends on a relaxation time as the only control parameter. The protocol comprises two fixed quenches and an intermediate relaxation time that determines the phase in which the quantum state is placed after the final quench. We apply it to an anharmonic Lipkin-Meshkov-Glick model. This model displays two excited-state quantum phase transitions which split the spectrum into three different phases: two of them are symmetry-breaking phases, and one is a disordered phase. As a consequence, our protocol induces several kind of dynamical phase transitions. We characterize all of them in terms of the constants of motion characterizing all three phases of the model.

7.Quantum simulation of the 1D Fermi-Hubbard model as a $\mathrm{Z}_2$ lattice-gauge theory

Authors:Uliana E. Khodaeva, Dmitry L. Kovrizhin, Johannes Knolle

Abstract: The Fermi-Hubbard model is one of the central paradigms in the physics of strongly-correlated quantum many-body systems. Here we propose a quantum circuit algorithm based on the $\mathrm{Z}_2$ lattice gauge theory (LGT) representation of the one-dimensional Fermi-Hubbard model, which is suitable for implementation on current NISQ quantum computers. Within the LGT description there is an extensive number of local conserved quantities commuting with the Hamiltonian. We show how these conservation laws can be used to implement an efficient error-mitigation scheme. The latter is based on a post-selection of states for noisy quantum simulators. While the LGT description requires a deeper quantum-circuit compared to a Jordan-Wigner (JW) based approach, remarkably, we find that our error-correction protocol leads to results being on-par or even better than a standard JW implementation on noisy quantum simulators.

8.Entangled coherent states and violations of Bell-CHSH inequalities

Authors:Philipe De Fabritiis, Fillipe M. Guedes, Giovani Peruzzo, Silvio P. Sorella

Abstract: Three classes of entangled coherent states are employed to study the Bell-CHSH inequality. By using pseudospin operators in infinite dimensional Hilbert spaces, four dichotomic operators $(A,A',B,B')$ entering the inequality are constructed. For each class of coherent states, we compute the correlator $\langle \psi \vert A B + A' B + A B' - A' B' \vert \psi \rangle$, analyzing the set of parameters that leads to a Bell-CHSH inequality violation and, particularly, to the saturation of Tsirelson's bound.

9.Operational Markovianization in Randomized Benchmarking

Authors:Pedro Figueroa-Romero, Miha Papič, Adrian Auer, Min-Hsiu Hsieh, Kavan Modi, Inés de Vega

Abstract: A crucial task to obtain optimal and reliable quantum devices is to quantify their overall performance. The average fidelity of quantum gates is a particular figure of merit that can be estimated efficiently by Randomized Benchmarking (RB). However, the concept of gate-fidelity itself relies on the crucial assumption that noise behaves in a predictable, time-local, or so-called Markovian manner, whose breakdown can naturally become the leading source of errors as quantum devices scale in size and depth. We analytically show that error suppression techniques such as Dynamical Decoupling (DD) and Randomized Compiling (RC) can operationally Markovianize RB: i) fast DD reduces non-Markovian RB to an exponential decay plus longer-time corrections, while on the other hand, ii) RC generally does not affect the average, but iii) it always suppresses the variance of such RB outputs. We demonstrate these effects numerically with a qubit noise model. Our results show that simple and efficient error suppression methods can simultaneously tame non-Markovian noise and allow for standard and reliable gate quality estimation, a fundamentally important task in the path toward fully functional quantum devices.

10.Robust oracle quantum-state preparation via quantum signal processing

Authors:Lorenzo Laneve

Abstract: Oracle quantum state preparation is a variant of quantum state preparation where we want to construct a state $|\psi_c\rangle \propto \sum_x c(x) |x\rangle$ with the amplitudes $c(x)$ given as a (quantum) oracle. This variant is particularly useful when the quantum state has a short and simple classical description. We use recent techniques, namely quantum signal processing (QSP) and quantum singular value transform (QSVT), to construct a new algorithm that uses a polynomial number of qubits and oracle calls to construct $|\psi_c\rangle$. For a large class of states, this translates to an algorithm that is polynomial in the number of qubits, both in depth and width.

11.Probing gravity-related decoherence with a 16 $μ$g Schrödinger cat state

Authors:Matteo Fadel

Abstract: The Schr\"odinger equation predicts the validity of the superposition principle at any scale, yet we do not experience cats being in a superposition of "dead" and "alive" in our everyday lives. Modifications to quantum theory at the fundamental level may be responsible for the objective collapse of the wave function above a critical mass, thereby breaking down the superposition principle and restoring classical behavior at the macroscopic scale. One possibility is that these modifications are related to gravity, as described by the Di\'osi-Penrose wavefunction collapse model. Here, we investigate this model using experimental measurements on the decoherence of a Schr\"odinger cat state of a mechanical resonator with an effective mass of 16 micrograms.

12.Folded Spectrum VQE : A quantum computing method for the calculation of molecular excited states

Authors:Lila Cadi Tazi, Alex J. W. Thom

Abstract: The recent developments of quantum computing present potential novel pathways for quantum chemistry, as the increased computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g. Quantum Phase Estimation) but the limited capabilities of current noisy intermediate scale quantum devices (NISQ) motivated the development of less demanding hybrid algorithms. In this context, the Variational Quantum Eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground state energy of small molecules. The current study investigates the Folded Spectrum (FS) method as an extension to the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy, using the same ansatz as for the ground state calculation. Inspired by the variance-based methods from the Quantum Monte Carlo literature, the FS method minimizes the energy variance, thus requiring a computationally expensive squared Hamiltonian. We alleviate this potentially poor scaling by employing a Pauli grouping procedure, identifying sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction of the computational cost. We apply the FS-VQE method to small molecules (H$_2$,LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators.

13.Decomposition Algorithm of an Arbitrary Pauli Exponential through a Quantum Circuit

Authors:Maximilian Balthasar Mansky, Victor Ramos Puigvert, Santiago Londoño Castillo, Claudia Linnhoff-Popien

Abstract: We review the staircase algorithm to decompose the exponential of a generalized Pauli matrix and we propose two alternative recursive methods which offer more efficient quantum circuits. The first algorithm we propose, defined as the inverted staircase algorithm, is more efficient in comparison to the standard staircase algorithm in the number of one-qubit gates, giving a polynomial improvement of n/2. For our second algorithm, we introduce fermionic SWAP quantum gates and a systematic way of generalizing these. Such fermionic gates offer a simplification of the number of quantum gates, in particular of CNOT gates, in most quantum circuits. Regarding the staircase algorithm, fermionic quantum gates reduce the number of CNOT gates in roughly n/2 for a large number of qubits. In the end, we discuss the difference between the probability outcomes of fermionic and non-fermionic gates and show that, in general, due to interference, one cannot substitute fermionic gates through non-fermionic gates without altering the outcome of the circuit.

14.Bursts of polarised single photons from atom-cavity sources

Authors:Jan Ole Ernst, Juan-Rafael Alvarez, Thomas D. Barrett, Axel Kuhn

Abstract: Photonic qubits play an instrumental role in the development of advanced quantum technolo- gies, including quantum networking, boson sampling and measurement based quantum computing. A promising framework for the deterministic production of indistinguishable single photons is an atomic emitter coupled to a single mode of a high finesse optical cavity. Polarisation control is an important cornerstone, particularly when the polarisation defines the state of a quantum bit. Here, we propose a scheme for producing bursts of polarised single photons by coupling a generalised atomic emitter to an optical cavity, exploiting a particular choice of quantisation axis. In connection with two re-preparation methods, simulations predict 10-photon bursts coincidence count rates on the order of 1 kHz with single 87Rb atoms trapped in a state of the art optical cavity. This paves the way for novel n-photon experiments with atom-cavity sources.

15.Tight Bounds for Quantum Phase Estimation and Related Problems

Authors:Nikhil S. Mande, Ronald de Wolf

Abstract: Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing. In the basic scenario, one is given black-box access to a unitary $U$, and an eigenstate $\lvert \psi \rangle$ of $U$ with unknown eigenvalue $e^{i\theta}$, and the task is to estimate the eigenphase $\theta$ within $\pm\delta$, with high probability. The cost of an algorithm for us will be the number of applications of $U$ and $U^{-1}$. We tightly characterize the cost of several variants of phase estimation where we are no longer given an arbitrary eigenstate, but are required to estimate the maximum eigenphase of $U$, aided by advice in the form of states (or a unitary preparing those states) which are promised to have at least a certain overlap $\gamma$ with the top eigenspace. We give algorithms and matching lower bounds (up to logarithmic factors) for all ranges of parameters. We show that a small number of copies of the advice state (or of an advice-preparing unitary) are not significantly better than having no advice at all. We also show that having lots of advice (applications of the advice-preparing unitary) does not significantly reduce cost, and neither does knowledge of the eigenbasis of $U$. As an immediate consequence we obtain a lower bound on the complexity of the Unitary recurrence time problem, matching an upper bound of She and Yuen~[ITCS'23] and resolving one of their open questions. Lastly, we show that a phase-estimation algorithm with precision $\delta$ and error probability $\epsilon$ has cost $\Omega\left(\frac{1}{\delta}\log\frac{1}{\epsilon}\right)$, matching an easy upper bound. This contrasts with some other scenarios in quantum computing (e.g., search) where error-reduction costs only a factor $O(\sqrt{\log(1/\epsilon)})$. Our lower bound technique uses a variant of the polynomial method with trigonometric polynomials.

1.Quantum battery based on dipole-dipole interaction and external driving field

Authors:Wuji Zhang, Shuyue Wang, Chunfeng Wu, Gangcheng Wang

Abstract: The Dicke model is a fundamental model in quantum optics, which describes the interaction between quantum cavity field and a large ensemble of two-level atoms. In this work, we propose an efficient charging quantum battery achieved by considering an extension Dicke model with dipole-dipole interaction and an external driving field. We focus on the influence of the atomic interaction and the driving field on the performance of the quantum battery during the charging process and find that the maximum stored energy exhibits a critical phenomenon. The maximum stored energy and maximum charging power are investigated by varying the number of atoms. When the coupling between atoms and cavity is not very strong, compared to the Dicke quantum battery, such quantum battery can achieve more stable and faster charging. In addition, the maximum charging power approximately satisfies a superlinear scaling relation $P_{\rm max}\varpropto\beta N^{\alpha}$, where the quantum advantage $\alpha=1.6$ can be reached via optimizing the parameters.

2.Nonreciprocal Entanglement in Cavity-Magnon Optomechanics

Authors:Jiaojiao Chen, Xiao-Gang Fan, Wei Xiong, Dong Wang, Liu Ye

Abstract: Cavity optomechanics, a promising platform to investigate macroscopic quantum effects, has been widely used to study nonreciprocal entanglement with Sagnec effect. Here we propose an alternative way to realize nonreciprocal entanglemment among magnons, photons, and phonons in a hybrid cavity-magnon optomechanics, where magnon Kerr effect is used. We show that the Kerr effect gives rise to a magnon frequency shift and an additional two-magnon effect. Both of them can be tuned from positive to negative via tuning the magectic field direction, leading to nonreciprocity. By tuning system parameters such as magnon frequency detuning or the coefficient of the two-magnon effect, bipartite and tripartite entanglements can be nonreciprocally enhanced. By further studying the defined bidirectional contrast ratio, we find that nonreciprocity in our system can be switch on and off, and can be engineered by the bath temperature. Our proposal not only provides a potential path to demonstrate nonreciprocal entanglement with the magnon Kerr effect, but also opens a direction to engineer and design diverse nonreciprocal devices in hybrid cavity-magnon optomechanics with nonlinear effects.

3.Whence Nonlocality?

Authors:Aurélien Drezet

Abstract: In this chapter we discuss the Einstein Podolsky Rosen theorem and its strong relation with Bell's theorem. We clarify some ambiguities concerning `local-realism' and emphasize that neither realism nor determinism nor counterfactual definiteness are prerequisite of these theorems.

4.Evidence that PUBO outperforms QUBO when solving continuous optimization problems with the QAOA

Authors:Jonas Stein, Farbod Chamanian, Maximilian Zorn, Jonas Nüßlein, Sebastian Zielinski, Michael Kölle, Claudia Linnhoff-Popien

Abstract: Quantum computing provides powerful algorithmic tools that have been shown to outperform established classical solvers in specific optimization tasks. A core step in solving optimization problems with known quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) is the problem formulation. While quantum optimization has historically centered around Quadratic Unconstrained Optimization (QUBO) problems, recent studies show, that many combinatorial problems such as the TSP can be solved more efficiently in their native Polynomial Unconstrained Optimization (PUBO) forms. As many optimization problems in practice also contain continuous variables, our contribution investigates the performance of the QAOA in solving continuous optimization problems when using PUBO and QUBO formulations. Our extensive evaluation on suitable benchmark functions, shows that PUBO formulations generally yield better results, while requiring less qubits. As the multi-qubit interactions needed for the PUBO variant have to be decomposed using the hardware gates available, i.e., currently single- and two-qubit gates, the circuit depth of the PUBO approach outscales its QUBO alternative roughly linearly in the order of the objective function. However, incorporating the planned addition of native multi-qubit gates such as the global Molmer-Sorenson gate, our experiments indicate that PUBO outperforms QUBO for higher order continuous optimization problems in general.

5.Erasure conversion in a high-fidelity Rydberg quantum simulator

Authors:Pascal Scholl, Adam L. Shaw, Richard Bing-Shiun Tsai, Ran Finkelstein, Joonhee Choi, Manuel Endres

Abstract: Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices and for the quest towards fault-tolerant quantum computation. Rydberg arrays have emerged as a prominent platform in this context with impressive system sizes and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution, a form of erasure error conversion. However, two-qubit entanglement fidelities in Rydberg atom arrays have lagged behind competitors and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator. We implement erasure conversion via fast imaging of alkaline-earth atoms, which leaves atoms in a metastable state unperturbed and yields additional information independent of the final qubit readout. When excising data with observed erasure errors, we achieve a lower-bound for the Bell state generation fidelity of ${\geq} 0.9971^{+10}_{-13}$, which improves to ${\geq}0.9985^{+7}_{-12}$ when correcting for remaining state preparation errors. We further demonstrate erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, where we explicitly differentiate erasure conversion of preparation and Rydberg decay errors. We unveil the otherwise hidden impact of these errors on the simulation outcome by evaluating correlations between erasures and the final readout as well as between erasures themselves. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the ${\sim} 0.999$ regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices.

6.Silicon photonics-integrated time-domain balanced homodyne detector in continuous-variable quantum key distribution

Authors:Yanxiang Jia, Xuyang Wang, Xiao Hu, Xin Hua, Yu Zhang, Xubo Guo, Shengxiang Zhang, Xi Xiao, Shaohua Yu, Jun Zou, Yongmin Li

Abstract: We designed and experimentally demonstrated a silicon photonics-integrated time-domain balanced homodyne detector (TBHD), whose optical part has dimensions of 1.5 mm * 0.4 mm. To automatically and accurately balance the detector, new variable optical attenuators were used, and a common mode rejection ratio of 86.9 dB could be achieved. In the quantum tomography experiment, the density matrix and Wigner function of a coherent state were reconstructed with 99.97 % fidelity. The feasibility of this TBHD in a continuous-variable quantum key distribution (CVQKD) system was also demonstrated. This facilitates the integration of the optical circuits of the CVQKD system based on the GG02 protocol on the silicon photonics chip using TBHD.

7.Invasiveness of non-equilibrium quantum thermometry

Authors:Francesco Albarelli, Matteo G. A. Paris, Bassano Vacchini, Andrea Smirne

Abstract: One of the main advantages expected from using quantum probes as thermometers is non invasiveness, i.e., a negligible perturbation to the thermal sample. However, invasiveness is rarely investigated explicitly. Here, focusing on a pure-dephasing spin probe in a bosonic sample, we show that there is a non-trivial relation between the information on the temperature gained by a quantum probe and the heat absorbed by the sample due to the interaction. We show that optimizing over the probing time, i.e. considering a time-optimal probing scheme, also has the benefit of limiting the heat absorbed by the sample in each shot of the experiment. For such time-optimal protocols, we show that it is advantageous to have very strong probe-sample coupling, since in this regime the accuracy increases linearly with the coupling strength, while the amount of heat per shot saturates to a finite value. Since in pure-dephasing models the absorbed heat corresponds to the external work needed to couple and decouple the probe and the sample, our results also represent a first step towards the analysis of the thermodynamic and energetic cost of quantum thermometry.

8.Bosonic Nevanlinna Analytic Continuation

Authors:Kosuke Nogaki, Hiroshi Shinaoka

Abstract: Analytical continuation (AC) connects theoretical calculations and experimentally measurable quantities. The recently proposed Nevanlinna AC method is capable of accurately reproducing the sharp features of spectral functions at high frequencies while maintaining the causality of the response function. However, their use is currently limited to fermions. Here, we present an extension of this method to bosons using the hyperbolic tangent trick, allowing us to transform bosons into auxiliary fermions to which the Nevanlinna analytic continuation can be applied.

9.Breaking the entangling gate speed limit for trapped-ion qubits using a phase-stable standing wave

Authors:S. Saner, O. Băzăvan, M. Minder, P. Drmota, D. J. Webb, G. Araneda, R. Srinivas, D. M. Lucas, C. J. Ballance

Abstract: All laser-driven entangling operations for trapped-ion qubits have hitherto been performed without control of the optical phase of the light field, which precludes independent tuning of the carrier and motional coupling. By placing $^{88}$Sr$^+$ ions in a $\lambda=674$ nm standing wave, whose relative position is controlled to $\approx\lambda/100$, we suppress the carrier coupling by a factor of $18$, while coherently enhancing the spin-motion coupling. We experimentally demonstrate that the off-resonant carrier coupling imposes a speed limit for conventional traveling-wave M{\o}lmer-S{\o}rensen gates; we use the standing wave to surpass this limit and achieve a gate duration of $15\ \mu$s, restricted by the available laser power.

10.Parallelization of frequency domain quantum gates: manipulation and distribution of frequency-entangled photon pairs generated by a 21 GHz silicon micro-resonator

Authors:Antoine Henry, Dario Fioretto, Lorenzo M. Procopio, Stéphane Monfray, Frédéric Boeuf, Laurent Vivien, Eric Cassan, Carlos Ramos, Kamel Bencheikh, Isabelle Zaquine, Nadia Belabas

Abstract: Harnessing the frequency dimension in integrated photonics offers key advantages in terms of scalability, noise resilience, parallelization and compatibility with telecom multiplexing techniques. Integrated ring resonators have been used to generate frequency-entangled states through spontaneous four-wave-mixing. However, state-of-the-art integrated resonators are limited by trade-offs in size, number of frequency modes and spectral separation. We have developed silicon ring resonators with a foot-print below 0.05 mm2 providing more than 70 frequency channels separated by 21 GHz. We exploit the narrow frequency separation to parallelize and independently control 34 single qubit-gates with off-the-shelf electro-optic devices. This allows to fully characterize 17 frequency-bin maximally-entangled qubit pairs by performing quantum state tomography. We demonstrate for the first time a fully connected 5-user quantum network in the frequency domain. These results are a step towards a new generation of quantum circuits implemented with scalable silicon photonics technology, for applications in quantum computing and secure communications.

11.Catalytic and asymptotic equivalence for quantum entanglement

Authors:Ray Ganardi, Tulja Varun Kondra, Alexander Streltsov

Abstract: Entanglement is a fundamental resource in quantum information processing, yet understanding its manipulation and transformation remains a challenge. Many tasks rely on highly entangled pure states, but obtaining such states is often challenging due to the presence of noise. Typically, entanglement manipulation procedures involving asymptotically many copies of a state are considered to overcome this problem. These procedures allow for distilling highly entangled pure states from noisy states, which enables a wide range of applications, such as quantum teleportation and quantum cryptography. When it comes to manipulating entangled quantum systems on a single copy level, using entangled states as catalysts can significantly broaden the range of achievable transformations. Similar to the concept of catalysis in chemistry, the entangled catalyst is returned unchanged at the end of the state manipulation procedure. Our results demonstrate that despite the apparent conceptual differences between the asymptotic and catalytic settings, they are actually strongly connected and fully equivalent for all distillable states. Our methods rely on the analysis of many-copy entanglement manipulation procedures which may establish correlations between different copies. As an important consequence, we demonstrate that using an entangled catalyst cannot enhance the asymptotic singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and asymptotic state transformations of entangled states, and highlight the importance of correlations in these processes.

12.Catalysis cannot overcome bound entanglement

Authors:Ludovico Lami, Bartosz Regula, Alexander Streltsov

Abstract: The use of ancillary quantum systems known as catalysts is known to be able to enhance the capabilities of entanglement transformations under local operations and classical communication. However, the limits of such advantages have not been determined, and in particular it is not known if such assistance can overcome the known restrictions on asymptotic transformation rates - notably the existence of bound entangled (undistillable) states. Here we establish a general limitation of entanglement catalysis: we show that catalytic transformations can never allow for the distillation of entanglement from a bound entangled state, even if the catalyst may become correlated with the system of interest, and even under permissive choices of free operations. This precludes the possibility that catalysis can make entanglement theory asymptotically reversible. Our methods are based on new asymptotic bounds for the distillable entanglement and entanglement cost assisted by correlated catalysts. Extending our methods beyond entanglement theory, we show that catalysts also cannot enable reversibility in the manipulation of quantum coherence, establishing even stronger restrictions on asymptotic catalytic transformations in this resource theory.

13.ResQNets: A Residual Approach for Mitigating Barren Plateaus in Quantum Neural Networks

Authors:Muhammad Kashif, Saif Al-kuwari

Abstract: The barren plateau problem in quantum neural networks (QNNs) is a significant challenge that hinders the practical success of QNNs. In this paper, we introduce residual quantum neural networks (ResQNets) as a solution to address this problem. ResQNets are inspired by classical residual neural networks and involve splitting the conventional QNN architecture into multiple quantum nodes, each containing its own parameterized quantum circuit, and introducing residual connections between these nodes. Our study demonstrates the efficacy of ResQNets by comparing their performance with that of conventional QNNs and plain quantum neural networks (PlainQNets) through multiple training experiments and analyzing the cost function landscapes. Our results show that the incorporation of residual connections results in improved training performance. Therefore, we conclude that ResQNets offer a promising solution to overcome the barren plateau problem in QNNs and provide a potential direction for future research in the field of quantum machine learning.

14.Coherent interface between optical and microwave photons on an integrated superconducting atom chip

Authors:David Petrosyan, József Fortágh, Gershon Kurizki

Abstract: Sub-wavelength arrays of atoms exhibit remarkable optical properties, analogous to those of phased array antennas, such as collimated directional emission or nearly perfect reflection of light near the collective resonance frequency. We propose to use a single-sheet sub-wavelength array of atoms as a switchable mirror to achieve a coherent interface between propagating optical photons and microwave photons in a superconducting coplanar waveguide resonator. In the proposed setup, the atomic array is located near the surface of the integrated superconducting chip containing the microwave cavity and optical waveguide. A driving laser couples the excited atomic state to Rydberg states with strong microwave transition. Then the presence or absence of a microwave photon in the superconducting cavity makes the atomic array transparent or reflective to the incoming optical pulses of proper frequency and finite bandwidth.

15.Collateral coupling between superconducting resonators: Fast and high fidelity generation of qudit-qudit entanglement

Authors:Pedro Rosario, Alan C. Santos, Celso Jorge Villas-Boas, Romain Bachelard

Abstract: Superconducting circuits are highly controllable platforms to manipulate quantum states, which make them particularly promising for quantum information processing. We here show how the existence of a distance-independent interaction between microwave resonators coupled capacitively through a qubit offers a new control parameter toward this goal. This interaction is able to induce an idling point between resonant resonators, and its state-dependent nature allows one to control the flow of information between the resonators. The advantage of this scheme over previous one is demonstrated through the generation of high-fidelity NOON states between the resonators, with a lower number of operations than previous schemes. Beyond superconducting circuits, our proposal could also apply to atomic lattices with clock transitions in optical cavities, for example.

16.Generalized Time-bin Quantum Random Number Generator with Uncharacterized Devices

Authors:Hamid Tebyanian, Mujtaba Zahidy, Ronny Müller, Søren Forchhammer, Davide Bacco, Leif. K. Oxenløwe

Abstract: Random number generators (RNG) based on quantum mechanics are captivating due to their security and unpredictability compared to conventional generators, such as pseudo-random number generators and hardware-random number generators. This work analyzes evolutions in the extractable amount of randomness with increasing the Hilbert space dimension, state preparation subspace, or measurement subspace in a class of semi-device-independent quantum-RNG, where bounding the states' overlap is the core assumption, built on the prepare-and-measure scheme. We further discuss the effect of these factors on the complexity and draw a conclusion on the optimal scenario. We investigate the generic case of time-bin encoding scheme, define various input (state preparation) and outcome (measurement) subspaces, and discuss the optimal scenarios to obtain maximum entropy. Several input designs were experimentally tested and analyzed for their conceivable outcome arrangements. We evaluated their performance by considering the device's imperfections, particularly the after-pulsing effect and dark counts of the detectors. Finally, we demonstrate that this approach can boost the system entropy, resulting in more extractable randomness.

17.Phase-locking an interferometer with single-photon detections

Authors:Bastian Hacker, Kevin Günthner, Conrad Rößler, Christoph Marquardt

Abstract: We report on a novel phase-locking technique for fiber-based Mach-Zehnder interferometers based on discrete single-photon detections, and demonstrate this in a setup. Our interferometer decodes relative-phase-encoded optical pulse pairs for quantum key distribution applications and requires no locking laser in addition to the weak received signal. Our new simple locking scheme is shown to produce an Ornstein-Uhlenbeck dynamic and achieve optimal phase noise for a given count rate. In case of wavelength drifts that arise during the reception of Doppler-shifted satellite signals, the arm-length difference gets continuously readjusted to keep the interferometer phase stable.

18.Suppression of dark-state polariton collapses in cold-atom quantum memory

Authors:Katja Gosar, Vesna Pirc Jevšenak, Tadej Mežnaršič, Samo Beguš, Tomasz Krehlik, Dušan Ponikvar, Erik Zupanič, Peter Jeglič

Abstract: We observe dark-state polariton collapses and revivals in a quantum memory based on electromagnetically induced transparency on a cloud of cold cesium atoms in a magnetic field. Using $\sigma^+$ polarized signal and control beams in the direction of the magnetic field, we suppress the dark-state polariton collapses by polarizing the atoms towards one of the stretched Zeeman states and optimizing the frequency detuning of the control beam. In this way, we demonstrate a quantum memory with only partial dark-state polariton collapses, making the memory usable at any storage time, not only at discretized times of revivals. We obtain storage time of more than 400 $\rm{\mu}$s, which is ten times longer than what we can achieve by trying to annul the magnetic field.

19.A Solvable Model of Quantum Darwinism-Encoding Transitions

Authors:Benoît Ferté, Xiangyu Cao

Abstract: We propose a solvable model of Quantum Darwinism to encoding transitions -- abrupt changes in how quantum information spreads in a many-body system under unitary dynamics. We consider a random Clifford circuit on an expanding tree, whose input qubit is entangled with a reference. The model has a Quantum Darwinism phase, where one classical bit of information about the reference can be retrieved from an arbitrarily small fraction of the output qubits, and an encoding phase where such retrieval is impossible. The two phases are separated by a mixed phase and two continuous transitions. We compare the exact result to a two-replica calculation. The latter yields a similar ``annealed'' phase diagram, which applies also to a model with Haar random unitaries. We relate our approach to measurement induced phase transitions (MIPTs), by solving a modified model where an environment eavesdrops on an encoding system. It has a sharp MIPT only with full access to the environment.

20.Stimulated emission of signal photons from dark matter waves

Authors:Ankur Agrawal, Akash V. Dixit, Tanay Roy, Srivatsan Chakram, Kevin He, Ravi K. Naik, David I. Schuster, Aaron Chou

Abstract: The manipulation of quantum states of light has resulted in significant advancements in both dark matter searches and gravitational wave detectors [1-4]. Current dark matter searches operating in the microwave frequency range use nearly quantum-limited amplifiers [3, 5, 6]. Future high frequency searches will use photon counting techniques [1] to evade the standard quantum limit. We present a signal enhancement technique that utilizes a superconducting qubit to prepare a superconducting microwave cavity in a non-classical Fock state and stimulate the emission of a photon from a dark matter wave. By initializing the cavity in an $|n=4\rangle$ Fock state, we demonstrate a quantum enhancement technique that increases the signal photon rate and hence also the dark matter scan rate each by a factor of 2.78. Using this technique, we conduct a dark photon search in a band around $\mathrm{5.965\, GHz \, (24.67\, \mu eV)}$, where the kinetic mixing angle $\epsilon \geq 4.35 \times 10^{-13}$ is excluded at the $90\%$ confidence level.

1.Mechanically Induced Correlated Errors on Superconducting Qubits with Relaxation Times Exceeding 0.4 Milliseconds

Authors:Shingo Kono, Jiahe Pan, Mahdi Chegnizadeh, Xuxin Wang, Amir Youssefi, Marco Scigliuzzo, Tobias J. Kippenberg

Abstract: Superconducting qubits are one of the most advanced candidates to realize scalable and fault-tolerant quantum computing. Despite recent significant advancements in the qubit lifetimes, the origin of the loss mechanism for state-of-the-art qubits is still subject to investigation. Moreover, successful implementation of quantum error correction requires negligible correlated errors among qubits. Here, we realize ultra-coherent superconducting transmon qubits based on niobium capacitor electrodes, with lifetimes exceeding 0.4 ms. By employing a nearly quantum-limited readout chain based on a Josephson traveling wave parametric amplifier, we are able to simultaneously record bit-flip errors occurring in a multiple-qubit device, revealing that the bit-flip errors in two highly coherent qubits are strongly correlated. By introducing a novel time-resolved analysis synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that a pulse tube mechanical shock causes nonequilibrium dynamics of the qubits, leading to correlated bit-flip errors as well as transitions outside of the computational state space. Our observations confirm that coherence improvements are still attainable in transmon qubits based on the superconducting material that has been commonly used in the field. In addition, our findings are consistent with qubit dynamics induced by two-level systems and quasiparticles, deepening our understanding of the qubit error mechanisms. Finally, these results inform possible new error-mitigation strategies by decoupling superconducting qubits from their mechanical environments.

2.Comparison of the Lifshitz Theory Using the Nonconventional Fit of Response Functions with Precise Measurements of the Casimir Force

Authors:G. L. Klimchitskaya, V. M. Mostepanenko

Abstract: It has been known that the fundamental Lifshitz theory, which is based on first principles of thermal quantum field theory, experiences difficulties when compared with precise measurements of the Casimir force. We analyze the nonconventional fit of response functions of many materials along the imaginary frequency axis to the empirical model of "modified" oscillators which was recently proposed in the literature. According to our results, this model is unacceptable because at high frequencies it leads to the asymptotic behavior of response functions which is in contradiction with that following from the fundamental physical principles. We calculate the Casimir interaction in the configurations of several precise experiments using the Lifshitz theory and the response functions to quantized electromagnetic field expressed in terms of modified oscillators and demonstrate that the obtained results are excluded by the measurement data. This invalidates a claim made in the literature that the Casimir-van der Waals forces calculated using these response functions are in remarkable agreement with the experimental values. Possible reasons for a disagreement between experiment and theory are discussed, and the way to improve the situation is directed.

3.The Quantum Internet: an Efficient Stabilizer states Distribution Scheme

Authors:Seid Koudia

Abstract: Quantum networks constitute a major part of quantum technologies. They will boost distributed quantum computing drastically by providing a scalable modular architecture of quantum chips, or by establishing an infrastructure for measurement based quantum computing. Moreover, they will provide the backbone of the future quantum internet, allowing for high margins of security. Interestingly, the advantages that the quantum networks would provide for communications, rely on entanglement distribution, which suffers from high latency in protocols based on Bell pair distribution and bipartite entanglement swapping. Moreover, the designed algorithms for multipartite entanglement routing suffer from intractability issues making them unsolvable exactly in polynomial time. In this paper, we investigate a new approach for graph states distribution in quantum networks relying inherently on local quantum coding -- LQC -- isometries and on multipartite states transfer. Additionally, single-shot bounds for stabilizer states distribution are provided. Analogously to network coding, these bounds are shown to be achievable if appropriate isometries/stabilizer codes in relay nodes are chosen, which induces a lower latency entanglement distribution. As a matter of fact, the advantages of the protocol for different figures of merit of the network are provided.

4.Pattern QUBOs: Algorithmic construction of 3SAT-to-QUBO transformations

Authors:Sebastian Zielinski, Jonas Nüßlein, Jonas Stein, Thomas Gabor, Claudia Linnhoff-Popien, Sebastian Feld

Abstract: 3SAT instances need to be transformed into instances of Quadratic Unconstrained Binary Optimization (QUBO) to be solved on a quantum annealer. Although it has been shown that the choice of the 3SAT-to-QUBO transformation can impact the solution quality of quantum annealing significantly, currently only a few 3SAT-to-QUBO transformations are known. Additionally, all of the known 3SAT-to-QUBO transformations were created manually (and not procedurally) by an expert using reasoning, which is a rather slow and limiting process. In this paper, we will introduce the name Pattern QUBO for a concept that has been used implicitly in the construction of 3SAT-to-QUBO transformations before. We will provide an in-depth explanation for the idea behind Pattern QUBOs and show its importance by proposing an algorithmic method that uses Pattern QUBOs to create new 3SAT-to-QUBO transformations automatically. As an additional application of Pattern QUBOs and our proposed algorithmic method, we introduce approximate 3SAT-to-QUBO transformations. These transformations sacrifice optimality but use significantly fewer variables (and thus physical qubits on quantum hardware) than non-approximate 3SAT-to-QUBO transformations. We will show that approximate 3SAT-to-QUBO transformations can nevertheless be very effective in some cases.

5.Speeding up quantum circuits simulation using ZX-Calculus

Authors:Tristan Cam, Simon Martiel

Abstract: We present a simple and efficient way to reduce the contraction cost of a tensor network to simulate a quantum circuit. We start by interpreting the circuit as a ZX-diagram. We then use simplification and local complementation rules to sparsify it. We find that optimizing graph-like ZX-diagrams improves existing state of the art contraction cost by several order of magnitude. In particular, we demonstrate an average contraction cost 1180 times better for Sycamore circuits of depth 20, and up to 4200 times better at peak performance.

6.Dissipative Quantum Hopfield Network: A numerical analysis

Authors:Joaquín J. Torres, Daniel Manzano

Abstract: We present extensive simulations of the recently reported quantum version of the well-known Hopfield Neural Network to explore its emergent behavior. The system is constituted of a network of $N$ qubits oscillating at a given $\Omega$ frequency and which are coupled via Lindblad jump operators that depend on local fields $h_i$ depending on some given stored patterns. In agreement with previous results, our simulations show pattern-antipattern oscillations of the overlaps with the stored patterns similar to those reported within a mean-field description of such a system, and which are due to metastability originated by the quantum effect driven by the $s_x^i$ qubit operators. In simulations, we observe that such oscillations are stochastic due to the inherent metastability of the pattern attractors induced by the quantum term and disappear in finite systems when one averages over many quantum trajectories. In addition, we report the system behavior when the number of stored patterns enlarges, for the minimum temperature we can reach in simulations (namely $T=0.005$). Our study reveals that the quantum term of the Hamiltonian has a negative effect on storage capacity, decreasing the overlap with the starting memory pattern for increased values of $\Omega$ and the number of stored patterns. However, although the initial pattern destabilizes due to quantum oscillations, other patterns can be retrieved and remain stable for a large number of stored patterns, implying a quantum-dependent nonlinear relationship between the recall process and the number of stored patterns.

7.Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions

Authors:Shi Jin, Xiantao Li, Nana Liu, Yue Yu

Abstract: This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and even alters the Hamiltonian structure of the dynamics when boundary and interface conditions are included. This seemingly intractable issue can be resolved by using a recently introduced Schr\"odingerisation method (Jin et al. 2022) -- it converts any linear PDEs and ODEs with non-Hermitian dynamics to a system of Schr\"odinger equations, via the so-called warped phase transformation that maps the equation into one higher dimension. We implement this method for several typical problems, including the linear convection equation with inflow boundary conditions and the heat equation with Dirichlet and Neumann boundary conditions. For interface problems, we study the (parabolic) Stefan problem, linear convection, and linear Liouville equations with discontinuous and even measure-valued coefficients. We perform numerical experiments to demonstrate the validity of this approach, which helps to bridge the gap between available quantum algorithms and computational models for classical and quantum dynamics with boundary and interface conditions.

8.Vibrational strong coupling in liquid water from cavity molecular dynamics

Authors:Annina Z. Lieberherr, Seth T. E. Furniss, Joseph E. Lawrence, David E. Manolopoulos

Abstract: We assess the cavity molecular dynamics method for the calculation of vibrational polariton spectra, using liquid water as a specific example. We begin by disputing a recent suggestion that nuclear quantum effects may lead to a broadening of polariton bands, finding instead that they merely result in anharmonic red shifts in the polariton frequencies. We go on to show that our simulated cavity spectra can be reproduced to graphical accuracy with a harmonic model that uses just the cavity-free spectrum and the geometry of the cavity as input. We end by showing that this harmonic model can be combined with the experimental cavity-free spectrum to give results in good agreement with optical cavity measurements. Since the input to our harmonic model is equivalent to the input to the transfer matrix method of applied optics, we conclude that cavity molecular dynamics cannot provide any more insight into the effect of vibrational strong coupling on the absorption spectrum than this transfer matrix method, which is already widely used by experimentalists to corroborate their cavity results.

9.Boosted Ensembles of Qubit and Continuous Variable Quantum Support Vector Machines for B Meson Flavour Tagging

Authors:Maxwell T. West, Martin Sevior, Muhammad Usman

Abstract: The recent physical realisation of quantum computers with dozens to hundreds of noisy qubits has given birth to an intense search for useful applications of their unique capabilities. One area that has received particular attention is quantum machine learning (QML), the study of machine learning algorithms running natively on quantum computers. Such algorithms have begun to be applied to data intensive problems in particle physics, driven by the expected increased capacity for pattern recognition of quantum computers. In this work we develop and apply QML methods to B meson flavour tagging, an important component of experiments in particle physics which probe heavy quark mixing and CP violation in order to obtain a better understanding of the matter-antimatter asymmetry observed in the universe. We simulate boosted ensembles of quantum support vector machines (QSVMs) based on both conventional qubit-based and continuous variable architectures, attaining effective tagging efficiencies of 28.0% and 29.2% respectively, comparable with the leading published result of 30.0% using classical machine learning algorithms. The ensemble nature of our classifier is of particular importance, doubling the effective tagging efficiency of a single QSVM, which we find to be highly prone to overfitting. These results are obtained despite the strong constraint of working with QSVM architectures that are classically simulable, and we find evidence that continuous variable QSVMs beyond the classically simulable regime may be able to realise even higher performance, surpassing the reported classical results, when sufficiently powerful quantum hardware is developed to execute them.

10.Reservoir-free decoherence in flying qubits

Authors:Nicolò Piccione, Léa Bresque, Andrew N. Jordan, Robert S. Whitney, Alexia Auffèves

Abstract: An effective time-dependent Hamiltonian can be implemented by making a quantum system fly through an inhomogeneous potential, realizing, for example, a quantum gate on its internal degrees of freedom. However, flying systems have a spatial spread that will generically entangle the internal and spatial degrees of freedom, leading to decoherence in the internal state dynamics, even in the absence of any external reservoir. We provide formulas valid at all times for the dynamics, fidelity, and change of entropy for small spatial spreads, quantified by $\Delta x$. This decoherence is non-Markovian and its effect can be significant for ballistic qubits (scaling as $\Delta x^2$) but not for qubits carried by a moving potential well (scaling as $\Delta x^6$). We also discuss a method to completely counteract this decoherence for a ballistic qubit later measured.

11.Variational Quantum Algorithms for Simulation of Lindblad Dynamics

Authors:Tasneem Watad, Netanel H. Lindner

Abstract: We introduce a variational hybrid classical-quantum algorithm to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our method is based on a direct representation of density matrices and quantum observables as quantum superstates. We design and optimize low-depth variational quantum circuits that efficiently capture the unitary and non-unitary dynamics of the solutions. We benchmark and test the algorithm on different system sizes, showing its potential for utility with near-future hardware.

12.Entanglement as a sufficient condition for quantum synchronization between two mechanical oscillators

Authors:Manju, Shubhrangshu Dasgupta, Asoka Biswas

Abstract: We present an optomechanical model to show that entanglement can be a sufficient condition for quantum synchronization of two mechanical oscillators. As both these entities can be characterized in terms of variances of a set of EPR-like conjugate quadratures, we investigate whether this leads to a specific condition for simultaneous existence of the both. In our model, one of the oscillators makes the cavity, while the other is kept suspended inside the cavity, and the always-on coupling between the two is mediated via the same cavity mode. We show that in presence of amplitude modulation with the same frequency as that of the oscillators, these oscillators get nearly complete quantum synchronized and entangled simultaneously in the steady state. We also show that entanglement always becomes accompanied by quantum synchronization, though the reverse is not necessarily true. Thus, entanglement becomes a sufficient condition for the quantum synchronization. This behaviour can be observed for a large range of system parameters.

13.Trainability barriers and opportunities in quantum generative modeling

Authors:Manuel S. Rudolph, Sacha Lerch, Supanut Thanasilp, Oriel Kiss, Sofia Vallecorsa, Michele Grossi, Zoë Holmes

Abstract: Quantum generative models, in providing inherently efficient sampling strategies, show promise for achieving a near-term advantage on quantum hardware. Nonetheless, important questions remain regarding their scalability. In this work, we investigate the barriers to the trainability of quantum generative models posed by barren plateaus and exponential loss concentration. We explore the interplay between explicit and implicit models and losses, and show that using implicit generative models (such as quantum circuit-based models) with explicit losses (such as the KL divergence) leads to a new flavour of barren plateau. In contrast, the Maximum Mean Discrepancy (MMD), which is a popular example of an implicit loss, can be viewed as the expectation value of an observable that is either low-bodied and trainable, or global and untrainable depending on the choice of kernel. However, in parallel, we highlight that the low-bodied losses required for trainability cannot in general distinguish high-order correlations, leading to a fundamental tension between exponential concentration and the emergence of spurious minima. We further propose a new local quantum fidelity-type loss which, by leveraging quantum circuits to estimate the quality of the encoded distribution, is both faithful and enjoys trainability guarantees. Finally, we compare the performance of different loss functions for modelling real-world data from the High-Energy-Physics domain and confirm the trends predicted by our theoretical results.

14.Classical analogs of generalized purities, entropies, and logarithmic negativity

Authors:Bogar Díaz, Diego González, Marcos J. Hernández, J. David Vergara

Abstract: It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by providing classical analogs of the generalized purities, Bastiaans-Tsallis entropies, R\'enyi entropies, and logarithmic negativity for classical integrable systems. These classical analogs are entirely characterized by the classical covariance matrix. We compute these classical analogs exactly in the cases of linearly coupled harmonic oscillators, a generalized harmonic oscillator chain, and a one-dimensional circular lattice of oscillators. In all of these systems, the classical analogs reproduce the results of their quantum counterparts whenever the system is in a Gaussian state. In this context, our results show that quantum information of Gaussian states can be reproduced by classical information.

15.Quantum Enhanced Probes of Magnetic Circular Dichroism

Authors:Chengyun Hua, Claire E. Marvinney, Seongjin Hong, Matthew Feldman, Yun-Yi Pai, Michael Chilcote, Joshua Rabinowitz, Raphael C. Pooser, Alberto Marino, Benjamin J. Lawrie

Abstract: Magneto-optical microscopies, including optical measurements of magnetic circular dichroism, are increasingly ubiquitous tools for probing spin-orbit coupling, charge-carrier g-factors, and chiral excitations in matter, but the minimum detectable signal in classical magnetic circular dichroism measurements is fundamentally limited by the shot-noise limit of the optical readout field. Here, we use a two-mode squeezed light source to improve the minimum detectable signal in magnetic circular dichroism measurements by 3 dB compared with state-of-the-art classical measurements, even with relatively lossy samples like terbium gallium garnet. We also identify additional opportunities for improvement in quantum-enhanced magneto-optical microscopies, and we demonstrate the importance of these approaches for environmentally sensitive materials and for low temperature measurements where increased optical power can introduce unacceptable thermal perturbations.

16.Versatile parametric coupling between two statically decoupled transmon qubits

Authors:X. Y. Jin, K. Cicak, Z. Parrott, S. Kotler, F. Lecocq, J. Teufel, J. Aumentado, E. Kapit, R. W. Simmonds

Abstract: Parametric coupling is a powerful technique for generating tunable interactions between superconducting circuits using only microwave tones. Here, we present a highly flexible parametric coupling scheme demonstrated with two transmon qubits, which can be employed for multiple purposes, including the removal of residual $ZZ$ coupling and the implementation of driven swap or swap-free controlled-$Z$ (c$Z$) gates. Our fully integrated coupler design is only weakly flux tunable, cancels static linear coupling between the qubits, avoids internal coupler dynamics or excitations, and operates with rf-pulses. We show that residual $ZZ$ coupling can be reduced with a parametric dispersive tone down to an experimental uncertainty of 5.5 kHz. Additionally, randomized benchmarking reveals that the parametric swap c$Z$ gate achieves a fidelity of 99.4% in a gate duration of 60 ns, while the dispersive parametric swap-free c$Z$ gate attains a fidelity of 99.5% in only 30 ns. We believe this is the fastest and highest fidelity gate achieved with on-chip parametric coupling to date. We further explore the dependence of gate fidelity on gate duration for both p-swap and p-swap-free c$Z$ gates, providing insights into the possible error sources for these gates. Overall, our findings demonstrate a versatility, precision, speed, and high performance not seen in previous parametric approaches. Finally, our design opens up new possibilities for creating larger, modular systems of superconducting qubits.

17.Repetitive readout and real-time control of nuclear spin qubits in $^{171}$Yb atoms

Authors:William Huie, Lintao Li, Neville Chen, Xiye Hu, Zhubing Jia, Won Kyu Calvin Sun, Jacob P. Covey

Abstract: We demonstrate high fidelity repetitive projective measurements of nuclear spin qubits in an array of neutral ytterbium-171 ($^{171}$Yb) atoms. We show that the qubit state can be measured with a fidelity of 0.995(4) under a condition that leaves it in the state corresponding to the measurement outcome with a probability of 0.993(6) for a single tweezer and 0.981(4) averaged over the array. This is accomplished by near-perfect cyclicity of one of the nuclear spin qubit states with an optically excited state under a magnetic field of $B=58$ G, resulting in a bright/dark contrast of $\approx10^5$ during fluorescence readout. The performance improves further as $\sim1/B^2$. The state-averaged readout survival of 0.98(1) is limited by off-resonant scattering to dark states and can be addressed via post-selection by measuring the atom number at the end of the circuit, or during the circuit by performing a measurement of both qubit states. We combine projective measurements with high-fidelity rotations of the nuclear spin qubit via an AC magnetic field to explore several paradigmatic scenarios, including the non-commutivity of measurements in orthogonal bases, and the quantum Zeno mechanism in which measurements "freeze" coherent evolution. Finally, we employ real-time feedforward to repetitively deterministically prepare the qubit in the $+z$ or $-z$ direction after initializing it in an orthogonal basis and performing a projective measurement in the $z$-basis. These capabilities constitute an important step towards adaptive quantum circuits with atom arrays, such as in measurement-based quantum computation, fast many-body state preparation, holographic dynamics simulations, and quantum error correction.

18.Verifiable blind quantum computing with trapped ions and single photons

Authors:P. Drmota, D. P. Nadlinger, D. Main, B. C. Nichol, E. M. Ainley, D. Leichtle, A. Mantri, E. Kashefi, R. Srinivas, G. Araneda, C. J. Ballance, D. M. Lucas

Abstract: We present the first hybrid matter-photon implementation of verifiable blind quantum computing. We use a trapped-ion quantum server and a client-side photonic detection system connected by a fibre-optic quantum network link. The availability of memory qubits and deterministic quantum logic enables interactive protocols without post-selection - a requirement for any scalable blind quantum cloud server which previous realisations could not provide. Our apparatus supports guaranteed privacy with <0.001 leaked bits per qubit and shows a clear path to fully verified quantum computing in the cloud.

19.Tackling the Qubit Mapping Problem with Permutation-Aware Synthesis

Authors:Ji Liu, Ed Younis, Mathias Weiden, Paul Hovland, John Kubiatowicz, Costin Iancu

Abstract: We propose a novel hierarchical qubit mapping and routing algorithm. First, a circuit is decomposed into blocks that span an identical number of qubits. In the second stage permutation-aware synthesis (PAS), each block is optimized and synthesized in isolation. In the third stage a permutation-aware mapping (PAM) algorithm maps the blocks to the target device based on the information from the second stage. Our approach is based on the following insights: (1) partitioning the circuit into blocks is beneficial for qubit mapping and routing; (2) with PAS, any block can implement an arbitrary input-output qubit mapping that reduces the gate count; and (3) with PAM, for two adjacent blocks we can select input-output permutations that optimize each block together with the amount of communication required at the block boundary. Whereas existing mapping algorithms preserve the original circuit structure and only introduce "minimal" communication via inserting SWAP or bridge gates, the PAS+PAM approach can additionally change the circuit structure and take full advantage of hardware-connectivity. Our experiments show that we can produce better-quality circuits than existing mapping algorithms or commercial compilers (Qiskit, TKET, BQSKit) with maximum optimization settings. For a combination of benchmarks we produce circuits shorter by up to 68% (18% on average) fewer gates than Qiskit, up to 36% (9% on average) fewer gates than TKET, and up to 67% (21% on average) fewer gates than BQSKit. Furthermore, the approach scales, and it can be seamlessly integrated into any quantum circuit compiler or optimization infrastructure.

20.Total correlation as a touchstone of dynamical quantum phase transition

Authors:Leela Ganesh Chandra Lakkaraju, Srijon Ghosh, Debasis Sadhukhan, Aditi Sen De

Abstract: A quantum many-body system undergoes phase transitions of distinct species with variations of local and global parameters. We propose a framework in which a dynamical quantity can change its behavior with the quenching of either global (coarse-grained criteria) or local system parameters (fine-grained criteria), revealing the transition points present in global ones. We illustrate our technique by employing a long-range extended Ising model in the presence of a transverse magnetic field which can be mapped to spinless fermions and hence can be investigated for large system size. We report that the scaling law followed by the total correlation, the composition of both quantum and classical correlations in the steady state, can identify the transition points at which the known indicators like rate function or entanglement length fail. Specifically, in a fine-grained scenario, total correlation either follows the same scaling law with the quenching at and across the critical points along the transverse magnetic field, or obeys the different laws, thereby establishing a transition in the range of interactions.

21.Hybrid quantum learning with data re-uploading on a small-scale superconducting quantum simulator

Authors:Aleksei Tolstobrov, Gleb Fedorov, Shtefan Sanduleanu, Shamil Kadyrmetov, Andrei Vasenin, Aleksey Bolgar, Daria Kalacheva, Viktor Lubsanov, Aleksandr Dorogov, Julia Zotova, Peter Shlykov, Aleksei Dmitriev, Konstantin Tikhonov, Oleg V. Astafiev

Abstract: Supervised quantum learning is an emergent multidisciplinary domain bridging between variational quantum algorithms and classical machine learning. Here, we study experimentally a hybrid classifier model accelerated by a quantum simulator - a linear array of four superconducting transmon artificial atoms - trained to solve multilabel classification and image recognition problems. We train a quantum circuit on simple binary and multi-label tasks, achieving classification accuracy around 95%, and a hybrid model with data re-uploading with accuracy around 90% when recognizing handwritten decimal digits. Finally, we analyze the inference time in experimental conditions and compare the performance of the studied quantum model with known classical solutions.

22.Squeezed Light Coexistence with Classical Communication over 10 km Optical Fiber

Authors:Adnan A. E. Hajomer, Huy Q. Nguyen, Melis Pahalı, Ulrik L. Andersen, Tobias Gehring

Abstract: We report the first coexistence experiment of 1550 nm single-mode squeezed states of light with a 1310 nm classical telecom channel over a 10 km fiber channel while measuring squeezing using a locally generated local oscillator. This is achieved using real-time optical heterodyne phase locking, allowing us to measure up to 0.5 dB of squeezing with a phase noise of 2.2 degrees.

23.A Modular Quantum Compilation Framework for Distributed Quantum Computing

Authors:Davide Ferrari, Stefano Carretta, Michele Amoretti

Abstract: For most practical applications, quantum algorithms require large resources in terms of qubit number, much larger than those available with current NISQ processors. With the network and communication functionalities provided by the Quantum Internet, Distributed Quantum Computing (DQC) is considered as a scalable approach for increasing the number of available qubits for computational tasks. For DQC to be effective and efficient, a quantum compiler must find the best partitioning for the quantum algorithm and then perform smart remote operation scheduling to optimize EPR pair consumption. At the same time, the quantum compiler should also find the best local transformation for each partition. In this paper we present a modular quantum compilation framework for DQC that takes into account both network and device constraints and characteristics. We implemented and tested a quantum compiler based on the proposed framework with some circuits of interest, such as the VQE and QFT ones, considering different network topologies, with quantum processors characterized by heavy hexagon coupling maps. We also devised a strategy for remote scheduling that can exploit both TeleGate and TeleData operations and tested the impact of using either only TeleGates or both. The evaluation results show that TeleData operations may have a positive impact on the number of consumed EPR pairs, while choosing a more connected network topology helps reduce the number of layers dedicated to remote operations.

24.Entanglement is indispensable for masking arbitrary set of quantum states

Authors:Debarupa Saha, Priya Ghosh, Ujjwal Sen

Abstract: We question the role of entanglement in masking quantum information contained in a set of mixed quantum states. We first show that a masker that can mask any two single-qubit pure states, can mask the entire set of mixed states comprising of the classical mixtures of those two pure qubit states as well. We then try to find the part played by entanglement in masking two different sets: One, a set of mixed states formed by the classical mixtures of two single-qubit pure commuting states, and another, a set of mixed states obtained by mixing two single-qubit pure non-commuting states. For both cases, we show that the masked states remain entangled unless the input state is an equal mixture of the two pure states. This in turn reveals that entanglement is necessary as well as sufficient for masking an arbitrary set of two single qubit states, regardless of their mixednesses and mutual commutativity.

25.Calibration of Syndrome Measurements in a Single Experiment

Authors:Christian Wimmer, Jochen Szangolies, Michael Epping

Abstract: Methods of quantum error correction are starting to be beneficial on current quantum computing hardware. Typically this requires to perform measurements which yield information about the occurred errors on the system. However, these syndrome measurements themselves introduce noise to the system. A full characterization of the measurements is very costly. Here we present a calibration method which allows to take the additional noise into account. Under reasonable assumptions we require only a single additional experiment. We give examples of how to apply this method to noise estimation and error correction. Finally we discuss the results of experiments carried out on an IBM quantum computer.

26.Further comments on "Is the moon there if nobody looks? Bell inequalities and physical reality"

Authors:Richard D. Gill

Abstract: Kupczynski (2023) claims that Gill and Lambare (2022a, 2022b) misrepresent several of his published papers. This paper shows that the latest version of his "contextuality by default" model of a Bell experiment places no constraints whatsoever on the statistics of observed results in Bell type experiments. It thereby effectively allows arbitrary non-locality, ie direct causal effects of local measurement settings on distant measurement outcomes.

27.Electronic Excited States from a Variance-Based Contracted Quantum Eigensolver

Authors:Yuchen Wang, David A. Mazziotti

Abstract: Electronic excited states of molecules are central to many physical and chemical processes, and yet they are typically more difficult to compute than ground states. In this paper we leverage the advantages of quantum computers to develop an algorithm for the highly accurate calculation of excited states. We solve a contracted Schr\"odinger equation (CSE) -- a contraction (projection) of the Schr\"odinger equation onto the space of two electrons -- whose solutions correspond identically to the ground and excited states of the Schr\"odinger equation. While recent quantum algorithms for solving the CSE, known as contracted quantum eigensolvers (CQE), have focused on ground states, we develop a CQE based on the variance that is designed to optimize rapidly to a ground or excited state. We apply the algorithm in a classical simulation without noise to computing the ground and excited states of H$_{4}$ and BH.

1.Quantum two-way time synchronization over a 103 km urban fiber

Authors:Huibo Hong, Runai Quan, Xiao Xiang, Yuting Liu, Tao Liu, Mingtao Cao, Ruifang Dong, Shougang Zhang

Abstract: As a new approach to realizing high-precision time synchronization between remote time scales, quantum two-way time synchronization via laboratory fiber link has shown significant enhancement of the synchronization stability to several tens of femtoseconds. To verify its great potential in practical systems, the field test in long-haul installed fiber optic infrastructure is required to be demonstrated. In this paper, we implement the two-way quantum time synchronization over a 103 km urban fiber link. A time synchronization stability of 3.67 ps at 10 s and 0.28 ps at 40000 s has been achieved, despite the large attenuation of 38 dB leading to fewer than 40 correlated events per second. This achievement marks the first successful step of quantum two-way time synchronization in the task of high-precision long-distance field synchronization systems.

2.Controlled entanglement source for quantum cryptography

Authors:Qiang Zeng, Haoyang Wang, Huihong Yuan, Yuanbin Fan, Lai Zhou, Yuanfei Gao, Haiqiang Ma, Zhiliang Yuan

Abstract: Quantum entanglement has become an essential resource in quantum information processing. Existing works employ entangled quantum states to perform various tasks, while little attention is paid to the control of the resource. In this work, we propose a simple protocol to upgrade an entanglement source with access control through phase randomization at the optical pump. The enhanced source can effectively control all users in utilizing the entanglement resource to implement quantum cryptography. In addition, we show this control can act as a practical countermeasure against memory attack on device-independent quantum key distribution at a negligible cost. To demonstrate the feasibility of our protocol, we implement an experimental setup using just off-the-shelf components and characterize its performance accordingly.

3.Non-Gaussian reconciliation for continuous-variable quantum key distribution

Authors:Xiangyu Wang, Menghao Xu, Yin Zhao, Ziyang Chen, Song Yu, Hong Guo

Abstract: Non-Gaussian modulation can improve the performance of continuous-variable quantum key distribution (CV-QKD). For Gaussian modulated coherent state CV-QKD, photon subtraction can realize non-Gaussian modulation, which can be equivalently implemented by non-Gaussian postselection. However, non-Gaussian reconciliation has not been deeply researched, which is one of the key technologies in CV-QKD. In this paper, we propose a non-Gaussian reconciliation method to obtain identical keys from non-Gaussian data. Multidimensional reconciliation and multi-edge type low density parity check codes (MET-LDPC) are used in non-Gaussian reconciliation scheme, where the layered belief propagation decoding algorithm of MET-LDPC codes is used to reduce the decoding complexity. Furthermore, we compare the error correction performance of Gaussian data and non-Gaussian data. The results show that the error correction performance of non-Gaussian data is better than Gaussian data, where the frame error rate can be reduced by 50% for code rate 0.1 at SNR of 0.1554 and the average iteration number can be reduced by 25%.

4.Experimental upstream transmission of continuous variable quantum key distribution access network

Authors:Xiangyu Wang, Ziyang Chen, Zhenghua Li, Dengke Qi, Song Yu, Hong Guo

Abstract: Continuous-variable quantum key distribution which can be implemented using only low-cost and off-the-shelf components reveals great potential in the practical large-scale realization. Access network as a modern network necessity, connects multiple end-users to the network backbone. In this work, we demonstrate the first upstream transmission quantum access networks using continuous-variable quantum key distribution. A two-end-user quantum access network is then experimentally realized. Through phase compensation, data synchronization and other technical upgrades, we achieve 390kbps secret key rate of the total network. In addition, we extend the case of two-end-user quantum access network to the case of multiple users, and analyze the network capacity in the case of multiple users by measuring the additive excess noise from different time slots.

5.Fundamental limits on quantum cloning from the no-signalling principle

Authors:Yanglin Hu, Marco Tomamichel

Abstract: The no-cloning theorem is a cornerstone of quantum cryptography. Here we generalize and rederive under weaker assumptions various upper bounds on the maximum achievable fidelity of probabilistic and deterministic cloning machines. Building on ideas by Gisin [Phys.~Lett.~A, 1998], our results hold even for cloning machines that do not obey the laws of quantum mechanics, as long as remote state preparation is possible and the non-signalling principle holds. We apply our general theorem to several subsets of states that are of interest in quantum cryptography.

6.[email protected]: Online Admission Control of Edge Applications with QKD-secured Communications

Authors:Claudio Cicconetti, Marco Conti, Andrea Passarella

Abstract: Quantum Key Distribution (QKD) enables secure communications via the exchange of cryptographic keys exploiting the properties of quantum mechanics. Nowadays the related technology is mature enough for production systems, thus field deployments of QKD networks are expected to appear in the near future, starting from local/metropolitan settings, where edge computing is already a thriving reality. In this paper, we investigate the interplay of resource allocation in the QKD network vs. edge nodes, which creates unique research challenges. After modeling mathematically the problem, we propose practical online policies for admitting edge application requests, which also select the edge node for processing and the path in the QKD network. Our simulation results provide initial insights into this emerging topic and lead the way to upcoming studies on the subject.

7.Multi-Valued Quantum Neurons

Authors:M. W. AlMasri

Abstract: The multiple-valued quantum logic is formulated in a systematic way using the Bargmann representation of quantum basis states. In this approach, the truth values or distinguish states are represented naturally as unique roots of unity placed on the unit circle. Consequently, multi-valued quantum neurons are based on the principles of multiple-valued threshold logic over the field of complex numbers. The training of MVQN is reduced to the movement along the unit circle. A quantum neural networks (QNNs) based on multi-valued quantum neurons can be constructed with complex weights, inputs, outputs encoded by roots of unity and activation function which maps the complex plane into the unit circle. Such neural networks enjoys fast convergence and higher functionalities comparing with quantum neural networks based on binary input with the same number of neurons and layers. Possible practical manipulation can be found using the orbital angular momentum (OAM) of light based QNNs.

8.Towards Deep Learning-Based Quantum Algorithms for Solving Nonlinear Partial Differential Equations

Authors:Lukas Mouton, Florentin Reiter, Ying Chen, Patrick Rebentrost

Abstract: Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the potential for enhancing a classical deep learning-based method for solving high-dimensional nonlinear partial differential equations with suitable quantum subroutines. First, with near-term noisy intermediate-scale quantum computers in mind, we construct architectures employing variational quantum circuits and classical neural networks in conjunction. While the hybrid architectures show equal or worse performance than their fully classical counterparts in simulations, they may still be of use in very high-dimensional cases or if the problem is of a quantum mechanical nature. Next, we identify the bottlenecks imposed by Monte Carlo sampling and the training of the neural networks. We find that quantum-accelerated Monte Carlo methods, as well as classical multi-level Monte Carlo methods, offer the potential to speed up the estimation of the loss function. In addition, we identify and analyse the trade-offs when using quantum-accelerated Monte Carlo methods to estimate the gradients with different methods, including a recently-developed back propagation-free forward gradient method. Finally, we discuss the usage of a suitable quantum algorithm for accelerating the training of feed-forward neural networks. Hence, this work provides different avenues with the potential for polynomial speedups for deep learning-based methods for nonlinear partial differential equations.

9.Kinetic energy equipartition: a tool to characterize quantum thermalization

Authors:Carlos F. Destefani, Xavier Oriols

Abstract: The Orthodox kinetic energy has, in fact, two hidden-variable components: one linked to the current (or Bohmian) velocity, and another linked to the osmotic velocity (or quantum potential), and which are respectively identified with phase and amplitude of the wavefunction. Inspired by Bohmian and Stochastic quantum mechanics, we address what happens to each of these two velocity components when the Orthodox kinetic energy thermalizes in closed systems, and how the pertinent weak values yield experimental information about them. We show that, after thermalization, the expectation values of both the (squared) current and osmotic velocities approach the same stationary value, that is, each of the Bohmian kinetic and quantum potential energies approaches half of the Orthodox kinetic energy. Such a `kinetic energy equipartition' is a novel signature of quantum thermalization that can empirically be tested in the laboratory, following a well-defined operational protocol as given by the expectation values of (squared) real and imaginary parts of the local-in-position weak value of the momentum, which are respectively related to the current and osmotic velocities. Thus, the kinetic energy equipartion presented here is independent on any ontological status given to these hidden variables, and it could be used as a novel element to characterize quantum thermalization in the laboratory, beyond the traditional use of expectation values linked to Hermitian operators. Numerical results for the nonequilibrium dynamics of a few-particle harmonic trap under random disorder are presented as illustration. And the advantages in using the center-of-mass frame of reference for dealing with systems with many indistinguishable particles are also discussed.

10.Scalable noisy quantum circuits for biased-noise qubits

Authors:Marco Fellous-Asiani, Moein Naseri, Chandan Datta, Alexander Streltsov, Michał Oszmaniec

Abstract: Quantum error mitigation allows to reduce the impact of noise on quantum algorithms. Yet, it is not scalable as it requires resources scaling exponentially with the circuit size. In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard-tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial overhead in algorithm repetitions. On the flip side we also found a classical algorithm able to efficiently simulate our specific variants of Hadamard test. We propose to use this algorithm as a simple benchmark of the biasness of the noise at the scale of large and complicated quantum circuits. The strong noise-resilience of our circuits could motivate further research, to see if a quantum computational advantage could be reached for highly specific, yet noisy circuits.

11.Counterdiabatic driving for long-lived singlet state preparation

Authors:Abhinav Suresh, Vishal Varma, Priya Batra, T S Mahesh

Abstract: The quantum adiabatic method, which maintains populations in their instantaneous eigenstates throughout the state evolution, is an established and often a preferred choice for state preparation and manipulation. Though it minimizes the driving cost significantly, its slow speed is a severe limitation in noisy intermediate-scale quantum (NISQ) era technologies. Since adiabatic paths are extensive in many physical processes, it is of broader interest to achieve adiabaticity at a much faster rate. Shortcuts to adiabaticity techniques which overcome the slow adiabatic process by driving the system faster through non-adiabatic paths, have seen increased attention recently. The extraordinarily long lifetime of the long-lived singlet states (LLS) in nuclear magnetic resonance, established over the past decade, has opened several important applications ranging from spectroscopy to biomedical imaging. Various methods, including adiabatic methods, are already being used to prepare LLS. In this article, we report the use of counterdiabatic driving (CD) to speed up LLS preparation with faster drives. Using NMR experiments, we show that CD can give stronger LLS order in shorter durations than conventional adiabatic driving.

12.Experimental quantum state transfer of an arbitrary single-qubit state on a cycle with four vertices using a coined quantum random walk

Authors:Gayatri Singh, Kavita Dorai, Arvind

Abstract: We experimentally demonstrate the transfer of an unknown single-qubit state from Alice to Bob via a two-step discrete-time quantum random walk on a cycle with four vertices on a four-qubit nuclear magnetic resonance quantum processor. The qubits with Alice and Bob are used as coin qubits and the walk is carried out on in a two-qubit `Gaming Arena'. In this scheme, the required entangled state is generated naturally via conditional shift operators during the quantum walk, instead of being prepared in advance. We implement controlled operators at Bob's end, which are controlled by Alice's coin qubit and arena qubits, in order to reconstruct Alice's randomly generated state at Bob's end. To characterize the state transfer process, we perform quantum process tomography by repeating the experiment for a set of input states $\{ \vert 0\rangle, \vert 1\rangle, \vert +\rangle, \vert -\rangle \}$. Using an entanglement witness, we certify that the quantum walk generates a genuine quadripartite entangled state of all four qubits. To evaluate the efficacy of the transfer scheme, We use quantum state tomography to reconstruct the transferred state by calculating the projection of the experimentally reconstructed four-qubit density matrix onto three-qubit basis states. Our results demonstrate that the quantum circuit is able to perform quantum state transfer via the two-step quantum random walk with high fidelity.

13.Asymmetric quantum decision-making

Authors:Honoka Shiratori, Hiroaki Shinkawa, André Röhm, Nicolas Chauvet, Etsuo Segawa, Jonathan Laurent, Guillaume Bachelier, Tomoki Yamagami, Ryoichi Horisaki, Makoto Naruse

Abstract: Collective decision-making is crucial to information and communication systems. Decision conflicts among agents hinder the maximization of potential utilities of the entire system. Quantum processes can realize conflict-free joint decisions among two agents using the entanglement of photons or quantum interference of orbital angular momentum (OAM). However, previous studies have always presented symmetric resultant joint decisions. Although this property helps maintain and preserve equality, it cannot resolve disparities. Global challenges, such as ethics and equity, are recognized in the field of responsible artificial intelligence as responsible research and innovation paradigm. Thus, decision-making systems must not only preserve existing equality but also tackle disparities. This study theoretically and numerically investigates asymmetric collective decision-making using quantum interference of photons carrying OAM or entangled photons. Although asymmetry is successfully realized, a photon loss is inevitable in the proposed models. The available range of asymmetry and method for obtaining the desired degree of asymmetry are analytically formulated.

14.Approximate quantum error correction, covariance symmetry and their relation

Authors:Hao Dai

Abstract: To perform reliable quantum computation, quantum error correction is indispensable. In certain cases, continuous covariance symmetry of the physical system can make exact error correction impossible. In this work, we study the approximate error correction and covariance symmetry from the information-theoretic perspective. For general encoding and noise channels, we define a quantity named infidelity to characterize the performance of the approximate quantum error correction and quantify the noncovariance of an encoding channel from the asymmetry measure of the corresponding Choi state. Particularly, when the encoding channel is isometric, we derive a trade-off relation between infidelity and noncovariance. Furthermore, we calculate the average infidelity and noncovariance measure for a type of random code.

15.Quantum Inspired Optimization for Industrial Scale Problems

Authors:William P. Banner, Shima Bab Hadiashar, Grzegorz Mazur, Tim Menke, Marcin Ziolkowski, Ken Kennedy, Jhonathan Romero, Yudong Cao, Jeffrey A. Grover, William D. Oliver

Abstract: Model-based optimization, in concert with conventional black-box methods, can quickly solve large-scale combinatorial problems. Recently, quantum-inspired modeling schemes based on tensor networks have been developed which have the potential to better identify and represent correlations in datasets. Here, we use a quantum-inspired model-based optimization method TN-GEO to assess the efficacy of these quantum-inspired methods when applied to realistic problems. In this case, the problem of interest is the optimization of a realistic assembly line based on BMW's currently utilized manufacturing schedule. Through a comparison of optimization techniques, we found that quantum-inspired model-based optimization, when combined with conventional black-box methods, can find lower-cost solutions in certain contexts.

16.Accessing continuous-variable entanglement witnesses with multimode spin observables

Authors:Célia Griffet, Tobias Haas, Nicolas J. Cerf

Abstract: We present several measurement schemes for accessing separability criteria for continuous-variable bipartite quantum systems. Starting from moments of the bosonic mode operators, criteria suitable to witness entanglement are expressed in terms of multimode spin observables via the Jordan-Schwinger map. These observables are typically defined over a few replicas of the state of interest and can be transformed into simple photon-number measurements by passive optical circuits. Our measurement schemes require only a handful of measurements, thereby allowing one to efficiently detect entanglement without the need for costly state tomography as illustrated for a variety of physically relevant states (Gaussian, mixed Schr\"odinger cat, and NOON states). The influence of typical experimental imperfections is shown to be moderate.

17.One-dimensional scattering of fermions in double Dirac delta potentials

Authors:Lucía Santamaría-Sanz

Abstract: The spectrum of bound and scattering states of the one dimensional Dirac Hamiltonian describing fermions distorted by a static background built from two Dirac delta potentials is studied. A distinction will be made between mass-spike and electrostatic Dirac delta-potentials. The second quantisation is then performed to promote the relativistic quantum mechanical problem to a relativistic Quantum Field Theory and study the quantum vacuum interaction energy for fermions confined between opaque plates.

18.JaqalPaw: A Guide to Defining Pulses and Waveforms for Jaqal

Authors:Daniel Lobser, Joshua Goldberg, Andrew J. Landahl, Peter Maunz, Benjamin C. A. Morrison, Kenneth Rudinger, Antonio Russo, Brandon Ruzic, Daniel Stick, Jay Van Der Wall, Susan M. Clark

Abstract: One of the many challenges of developing an open user testbed such as QSCOUT is providing an interface that maintains simplicity without compromising expressibility or control. This interface comprises two distinct elements: a quantum assembly language designed for specifying quantum circuits at the gate level, and a low-level counterpart used for describing gates in terms of waveforms that realize specific quantum operations. Jaqal, or "Just another quantum assembly language," is the language used in QSCOUT for gate-level descriptions of quantum circuits. JaqalPaw, or "Jaqal pulses and waveforms," is its pulse-level counterpart. This document concerns the latter, and presents a description of the tools needed for precisely defining the underlying waveforms associated with a gate primitive.

19.Localization Driven Quantum Sensing

Authors:Ayan Sahoo, Utkarsh Mishra, Debraj Rakshit

Abstract: We show that the delocalization-localization transition in a quantum-many body (QMB) systems is a compelling quantum resource for achieving quantum-enhanced sensitivity in parameter estimation. We exploit the vulnerability of a near-transition QMB state against the parameter shift for devising efficient sensing tools. In this realm the main focus of this work is to identify, propose and analyze experimentally relevant quantum observables for precision measurement. Taking a QMB system as a Fermi lattice under quasi-periodic modulation that supports an energy-independent delocalization-localization transition, we suggest operator-based adiabatic and dynamical quantum sensors endowed with considerable quantum advantages.

1.Low noise quantum frequency conversion of photons from a trapped barium ion to the telecom O-band

Authors:Uday Saha, James D. Siverns, John Hannegan, Qudsia Quraishi, Edo Waks

Abstract: Trapped ions are one of the leading candidates for scalable and long-distance quantum networks because of their long qubit coherence time, high fidelity single- and two-qubit gates, and their ability to generate photons entangled with the qubit state of the ion. One method for creating ion-photon entanglement is to exploit optically transitions from the P_(1/2) to S_(1/2) levels, which naturally emit spin-photon entangled states. But these optical transitions typically lie in the ultra-violet and visible wavelength regimes. These wavelengths exhibit significant fiber-optic propagation loss, thereby limiting the transfer of quantum information to tens of meters. Quantum frequency conversion is essential to convert these photons to telecom wavelengths so that they can propagate over long distances in fiber-based networks, as well as for compatibility with the vast number of telecom-based opto-electronic components. Here, we generate O-band telecom photons via a low noise quantum frequency conversion scheme from photons emitted from the P_(1/2) to S_(1/2) dipole transition of a trapped barium ion. We use a two-stage quantum frequency conversion scheme to achieve a frequency shift of 375.4 THz between the input visible photon and the output telecom photon achieving a conversion efficiency of 11%. We attain a signal-to-background ratio of over 100 for the converted O-band telecom photon with background noise less than 15 counts/sec. These results are an important step toward achieving trapped ion quantum networks over long distances for distributed quantum computing and quantum communication.

2.Steady-state Quantum Thermodynamics with Synthetic Negative Temperatures

Authors:Mohit Lal Bera, Tanmoy Pandit, Kaustav Chatterjee, Varinder Singh, Maciej Lewenstein, Utso Bhattacharya, Manabendra Nath Bera

Abstract: A bath with a negative temperature is a subject of intense debate in recent times. It raises fundamental questions not only on our understanding of negative temperature of a bath in connection with thermodynamics but also on the possibilities of constructing devices using such baths. In this work, we study steady-state quantum thermodynamics involving baths with negative temperatures. A bath with a negative temperature is created synthetically using two baths of positive temperatures and weakly coupling these with a qutrit system. These baths are then coupled to each other via a working system. At steady-state, the laws of thermodynamics are analyzed. We find that whenever the temperatures of these synthetic baths are identical, there is no heat flow, which reaffirms the zeroth law. There is always a spontaneous heat flow for different temperatures. In particular, heat flows from a bath with a negative temperature to a bath with a positive temperature which, in turn, implies that a bath with a negative temperature is `hotter' than a bath with a positive temperature. This warrants an amendment in the Kelvin-Planck statement of the second law, as suggested in earlier studies. In all these processes, the overall entropy production is positive, as required by the Clausius statement of the second law. We construct continuous heat engines operating between positive and negative temperature baths. These engines yield maximum possible heat-to-work conversion efficiency, that is, unity. We also study the thermodynamic nature of heat from a bath with a negative temperature and find that it is thermodynamic work but with negative entropy.

3.Stark tuning of telecom single-photon emitters based on a single Er$^{3+}$

Authors:Jian-Yin Huang, Peng-Jun Liang, Liang Zheng, Pei-Yun Li, You-Zhi Ma, Duan-Chen Liu, Zong-Quan Zhou, Chuan-Feng Li, Guang-Can Guo

Abstract: The implementation of scalable quantum networks requires photons at the telecom band and long-lived spin coherence. The single Er$^{3+}$ in solid-state hosts is an important candidate that fulfills these critical requirements simultaneously. However, to entangle distant Er$^{3+}$ ions through photonic connections, the emission frequency of individual Er$^{3+}$ in solid-state matrix must be the same, which is challenging because the emission frequency of Er$^{3+}$ depends on its local environment. In this study, we propose and experimentally demonstrate the Stark tuning of the emission frequency of a single Er$^{3+}$ in a Y$_2$SiO$_5$ crystal by employing electrodes interfaced with a silicon photonic crystal cavity. We obtain a Stark shift of 182.9 $\pm$ 0.8 MHz which is approximately 27 times of the optical emission linewidth, demonstrating the promising applications in tuning the emission frequency of independent Er$^{3+}$ into the same spectral channels. Our results provide a useful solution for the construction of scalable quantum networks based on single Er$^{3+}$ and a universal tool for tuning the emission of individual rare-earth ions.

4.Short Technical Review of Four Different Quantum Systems: Comparative Analysis of Quantum Correlation, Signal-to-Noise Ratio, and Fidelity

Authors:Ahmad Salmanogli

Abstract: This technical review examines the different methods and approaches used to create microwave modes quantum correlation. Specifically, we consider the electro-opto-mechanical, optoelectronics, 4-coupled qubits, and InP HEMT coupled with two external oscillator methods, and evaluate their effectiveness for quantum applications. As these systems are open quantum systems, they interact with their environment and thermal bath. To ensure an accurate comparison, we analyze all systems using the same gauge. Thus, all systems are shortly introduced, the total Hamiltonian is theoretically derived, and finally, the system dynamics are analogously analyzed using the Lindblad master equation. We then calculate the quantum correlation between cavity modes, signal-to-noise ratio, and fidelity for each system to evaluate their performance. The study result shows that the strength and nature of the calculated quantities vary among the systems. One interesting result is the emergence of mixing behavior in the quantum correlation and signal-to-noise ratio for systems that use different cavities. It also identified a significant similarity between the 4-coupled qubits and InP HEMT coupled with external oscillators methods, where an avoided-level crossing occurs in the quantum correlation. Additionally, the study reveals that the signal-to-noise ratio and classical discord are more consistent than quantum discord.

5.Transformations between arbitrary (quantum) objects and the emergence of indefinite causality

Authors:Simon Milz, Marco Túlio Quintino

Abstract: Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels and channels with memory, and also higher-order operations such as superchannels, quantum combs, n-time processes, testers, and process matrices which may not respect a definite causal order. Deducing and characterising their structural properties in terms of linear and semidefinite constraints is not only of foundational relevance, but plays an important role in enabling the numerical optimization over sets of quantum objects and allowing simpler connections between different concepts and objects. Here, we provide a general framework to deduce these properties in a direct and easy to use way. Additionally, while primarily guided by practical quantum mechanical considerations, we extend our analysis to mappings between \textit{general} linear/affine spaces and derive their properties, opening the possibility for analysing sets which are not explicitly forbidden by quantum theory, but are still not much explored. Together, these results yield versatile and readily applicable tools for all tasks that require the characterization of linear transformations, in quantum mechanics and beyond. As an application of our methods, we discuss the emergence of indefinite causality in higher-order quantum transformation.

6.Quantum Circuit Implementation and Resource Analysis of LBlock and LiCi

Authors:XiaoYu Jing, YanJu Li, GuangYue Zhao, Huiqin Xie

Abstract: Due to Grover's algorithm, any exhaustive search attack of block ciphers can achieve a quadratic speed-up. To implement Grover,s exhaustive search and accurately estimate the required resources, one needs to implement the target ciphers as quantum circuits. Recently, there has been increasing interest in quantum circuits implementing lightweight ciphers. In this paper we present the quantum implementations and resource estimates of the lightweight ciphers LBlock and LiCi. We optimize the quantum circuit implementations in the number of gates, required qubits and the circuit depth, and simulate the quantum circuits on ProjectQ. Furthermore, based on the quantum implementations, we analyze the resources required for exhaustive key search attacks of LBlock and LiCi with Grover's algorithm. Finally, we compare the resources for implementing LBlock and LiCi with those of other lightweight ciphers.

7.Classification of real and complex 3-qutrit states

Authors:Sabino Di Trani, Willem A. de Graaf, Alessio Marrani

Abstract: In this paper we classify the orbits of the group SL(3,F)^3 on the space F^3\otimes F^3\otimes F^3 for F=C and F=R. This is known as the classification of complex and real 3-qutrit states. We also give an overview of physical theories where these classifications are relevant.

8.Design and Analysis of Genuine Entanglement Access Control for the Quantum Internet

Authors:Jessica Illiano, Marcello Caleffi, Michele Viscardi, Angela Sara Cacciapuoti

Abstract: Multipartite entanglement plays a crucial role for the design of the Quantum Internet, due to its peculiarities with no classical counterpart. Yet, for entanglement-based quantum networks, a key open issue is constituted by the lack of an effective entanglement access control (EAC) strategy for properly handling and coordinating the quantum nodes in accessing the entangled resource. In this paper, we design a quantum-genuine entanglement access control (EAC) to solve the contention problem arising in accessing a multipartite entangled resource. The proposed quantum-genuine EAC is able to: i) fairly select a subset of nodes granted with the access to the contended resource; ii) preserve the privacy and anonymity of the identities of the selected nodes; iii) avoid to delegate the signaling arising with entanglement access control to the classical network. We also conduct a theoretical analysis of noise effects on the proposed EAC. This theoretical analysis is able to catch the complex noise effects on the EAC through meaningful parameters.

9.Adiabatic ground state preparation of fermionic many-body systems from a two-body perspective

Authors:Dyon van Vreumingen, Kareljan Schoutens

Abstract: A well-known method to prepare ground states of fermionic many-body hamiltonians is adiabatic state preparation, in which an easy to prepare state is time-evolved towards an approximate ground state under a specific time-dependent hamiltonian. However, which path to take in the evolution is often unclear, and a direct linear interpolation, which is the most common method, may not be optimal. In this work, we explore new types of adiabatic paths based on an eigendecomposition of the coefficient tensor in the second quantised representation of the difference between the final and initial hamiltonian (the residual hamiltonian). Since there is an equivalence between this tensor and a projection of the residual hamiltonian onto the subspace of two particles, this approach is essentially a two-body spectral decomposition. We show how for general hamiltonians, the adiabatic time complexity may be upper bounded in terms of the number of one-body modes $L$ and a minimal gap $\Delta$ along the path. Our finding is that the complexity is determined primarily by the degree of pairing in the two-body states. As a result, systems whose two-body eigenstates are uniform superpositions of distinct fermion pairs tend to exhibit maximal complexity, which scales as $O(L^4/\Delta^3)$ in direct interpolation and $O(L^6/\Delta^3)$ in an evolution that follows a path along the corners of a hypercube in parameter space. The usefulness of our method is demonstrated through a few examples involving Fermi-Hubbard models where, due to symmetries, level crossings occur in direct interpolation. We show that our method of decomposing the residual hamiltonian and thereby deviating from a direct path appropriately breaks the relevant symmetries, thus avoiding level crossings and enabling an adiabatic passage.

10.Performance Analysis of Quantum Error-Correcting Codes via MacWilliams Identities

Authors:Diego Forlivesi, Lorenzo Valentini, Marco Chiani

Abstract: One of the main challenges for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing and quantum Internet. We analyze the performance of stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the undetectable errors of stabilizer codes based on the quantum MacWilliams identities. The WE is then used to evaluate the error rate of quantum codes under maximum likelihood decoding or, in the case of surface codes, under minimum weight perfect matching (MWPM) decoding. Our findings lead to analytical formulas for the performance of generic stabilizer codes, including the Shor code, the Steane code, as well as surface codes. For example, on a depolarizing channel with physical error rate $\rho \to 0$ it is found that the logical error rate $\rho_\mathrm{L}$ is asymptotically $\rho_\mathrm{L} \to 16.2 \rho^2$ for the $[[9,1,3]]$ Shor code, $\rho_\mathrm{L} \to 16.38 \rho^2$ for the $[[7,1,3]]$ Steane code, $\rho_\mathrm{L} \to 18.74 \rho^2$ for the $[[13,1,3]]$ surface code, and $\rho_\mathrm{L} \to 149.24 \rho^3$ for the $[[41,1,5]]$ surface code.

11.Experimental free-space quantum key distribution over a turbulent high-loss channel

Authors:Md Mehdi Hassan, Kazi Reaz, Adrien Green, Noah Crum, George Siopsis

Abstract: Free-space quantum cryptography plays an integral role in realizing a global-scale quantum internet system. Compared to fiber-based communication networks, free-space networks experience significantly less decoherence and photon loss due to the absence of birefringent effects in the atmosphere. However, the atmospheric turbulence contributes to deviation in transmittance distribution, which introduces noise and channel loss. Several methods have been proposed to overcome the low signal-to-noise ratio. Active research is currently focused on establishing secure and practical quantum communication in a high-loss channel, and enhancing the secure key rate by implementing bit rejection strategies when the channel transmittance drops below a certain threshold. By simulating the atmospheric turbulence using an acousto-optical-modulator (AOM) and implementing the prefixed-threshold real-time selection (P-RTS) method, our group performed finite-size decoy-state Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol for 19 dB channel loss. With better optical calibration and efficient superconducting nano-wire single photon detector (SNSPD), we have extended our previous work to 40 dB channel loss characterizing the transmittance distribution of our system under upper moderate turbulence conditions.

12.Aharonov-Bohm effect in Presence of Superconductors

Authors:L. O'Raifeartaigh, N. Straumann, A. Wipf

Abstract: The analysis of a previous paper, in which it was shown that the energy for the Aharonov-Bohm effect could be traced to the interaction energy between the magnetic field of the electron and the background magnetic field, is extended to cover the case in which the magnetic field of the electron is shielded from the background magnetic field by superconducting material. The paradox that arises from the fact that such a shielding would apparently preclude the possibility of an interaction energy is resolved and, within the limits of the ideal situation considered, the observed experimental result is derived.

13.Efficient estimation of quantum state k-designs with randomized measurements

Authors:Lorenzo Versini, Karim Alaa El-Din, Florian Mintert, Rick Mukherjee

Abstract: Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body thermalization and studying black hole information paradox. Although generating a fully random ensemble is almost impossible and experimentally challenging, approximations of it are just as useful and are known to emerge naturally in a variety of physical models, including Rydberg setups. These are referred to as approximate quantum state designs, and verifying their degree of randomness can be an expensive task, similar to performing full quantum state tomography on many-body systems. In this theoretical work, we efficiently validate the character of approximate quantum designs with respect to data size acquisition when compared to conventional frequentist approach. This is achieved by translating the information residing in the complex many-body state into a succinct representation of classical data using a random projective measurement basis, which is then processed, using methods of statistical inference including neural networks. Our scheme of combining machine learning methods for postprocessing the data obtained from randomized measurements for efficient characterisation of (approximate) quantum state k designs is applicable to any noisy quantum platform that can generate quantum designs.

14.Exploring the synergistic potential of quantum annealing and gate model computing for portfolio optimization

Authors:Naman Jain, M Girish Chandra

Abstract: Portfolio optimization is one of the most studied problems for demonstrating the near-term applications of quantum computing. However, large-scale problems cannot be solved on today's quantum hardware. In this work, we extend upon a study to use the best of both quantum annealing and gate-based quantum computing systems to enable solving large-scale optimization problems efficiently on the available hardware. The existing work uses a method called Large System Sampling Approximation (LSSA) that involves dividing the large problem into several smaller problems and then combining the multiple solutions to approximate the solution to the original problem. This paper introduces a novel technique to modify the sampling step of LSSA. We divide the portfolio optimization problem into sub-systems of smaller sizes by selecting a diverse set of assets that act as representatives of the entire market and capture the highest correlations among assets. We conduct tests on real-world stock data from the Indian stock market on up to 64 assets. Our experimentation shows that the hybrid approach performs at par with the traditional classical optimization methods with a good approximation ratio. We also demonstrate the effectiveness of our approach on a range of portfolio optimization problems of different sizes. We present the effects of different parameters on the proposed method and compare its performance with the earlier work. Our findings suggest that hybrid annealer-gate quantum computing can be a valuable tool for portfolio managers seeking to optimize their investment portfolios in the near future.

15.International time transfer between precise timing facilities secured with a quantum key distribution network

Authors:Francesco Picciariello, Francesco Vedovato, Davide Orsucci, Pablo Nahuel Dominguez, Thomas Zechel, Marco Avesani, Matteo Padovan, Giulio Foletto, Luca Calderaro, Daniele Dequal, Amita Shrestha, Ludwig Blumel, Johann Furthner, Giuseppe Vallone, Paolo Villoresi, Tobias D. Schmidt, Florian Moll

Abstract: Global Navigation Satellite Systems (GNSSs), such as GPS and Galileo, provide precise time and space coordinates globally and constitute part of the critical infrastructure of modern society. To reliably operate GNSS, a highly accurate and stable system time is required, such as the one provided by several independent clocks hosted in Precise Timing Facilities (PTFs) around the world. Periodically, the relative clock offset between PTFs is measured to have a fallback system to synchronize the GNSS satellite clocks. The security and integrity of the communication between PTFs is of paramount importance: if compromised, it could lead to disruptions to the GNSS service. Therefore, it is a compelling use-case for protection via Quantum Key Distribution (QKD), since this technology provides information-theoretic security. We have performed a field trial demonstration of such use-case by sharing encrypted time synchronization information between two PTFs, one located in Oberpfaffenhofen (Germany) and one in Matera (Italy) - more than 900km apart as the crow flies. To bridge this large distance, a satellite-QKD system is required, plus a "last-mile" terrestrial link to connect the optical ground station (OGS) to the actual location of the PTF. In our demonstration we have deployed two full QKD systems to protect the last-mile connection at both the locations and have shown via simulation that upcoming QKD satellites will be able to distribute keys between Oberpfaffenhofen and Matera exploiting already existing OGSs.

16.Learning Hard Distributions with Quantum-enhanced Variational Autoencoders

Authors:Anantha Rao, Dhiraj Madan, Anupama Ray, Dhinakaran Vinayagamurthy, M. S. Santhanam

Abstract: An important task in quantum generative machine learning is to model the probability distribution of measurements of many-body quantum systems. Classical generative models, such as generative adversarial networks (GANs) and variational autoencoders (VAEs), can model the distributions of product states with high fidelity, but fail or require an exponential number of parameters to model entangled states. In this paper, we introduce a quantum-enhanced VAE (QeVAE), a generative quantum-classical hybrid model that uses quantum correlations to improve the fidelity over classical VAEs, while requiring only a linear number of parameters. We provide a closed-form expression for the output distributions of the QeVAE. We also empirically show that the QeVAE outperforms classical models on several classes of quantum states, such as 4-qubit and 8-qubit quantum circuit states, haar random states, and quantum kicked rotor states, with a more than 2x increase in fidelity for some states. Finally, we find that the trained model outperforms the classical model when executed on the IBMq Manila quantum computer. Our work paves the way for new applications of quantum generative learning algorithms and characterizing measurement distributions of high-dimensional quantum states.

17.Probing critical states of matter on a digital quantum computer

Authors:Reza Haghshenas, Eli Chertkov, Matthew DeCross, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Nathan Hewitt, Chandler V. Horst, Mitchell Matheny, Tanner Mengle, Brian Neyenhuis, David Hayes, Michael Foss-Feig

Abstract: Although quantum mechanics underpins the microscopic behavior of all materials, its effects are often obscured at the macroscopic level by thermal fluctuations. A notable exception is a zero-temperature phase transition, where scaling laws emerge entirely due to quantum correlations over a diverging length scale. The accurate description of such transitions is challenging for classical simulation methods of quantum systems, and is a natural application space for quantum simulation. These quantum simulations are, however, not without their own challenges \textemdash~representing quantum critical states on a quantum computer requires encoding entanglement of a large number of degrees of freedom, placing strict demands on the coherence and fidelity of the computer's operations. Using Quantinuum's H1-1 quantum computer, we address these challenges by employing hierarchical quantum tensor-network techniques, creating the ground state of the critical transverse-field Ising chain on 128-sites with sufficient fidelity to extract accurate critical properties of the model. Our results suggest a viable path to quantum-assisted tensor network contraction beyond the limits of classical methods.

1.Noise is resource-contextual in quantum communication

Authors:Aditya Nema, Ananda G. Maity, Sergii Strelchuk, David Elkouss

Abstract: Estimating the information transmission capability of a quantum channel remains one of the fundamental problems in quantum information processing. In contrast to classical channels, the information-carrying capability of quantum channels is contextual. One of the most significant manifestations of this is the superadditivity of the channel capacity: the capacity of two quantum channels used together can be larger than the sum of the individual capacities. Here, we present a one-parameter family of channels for which as the parameter increases its one-way quantum and private capacities increase while its two-way capacities decrease. We also exhibit a one-parameter family of states with analogous behavior with respect to the one- and two-way distillable entanglement and secret key. Our constructions demonstrate that noise is context dependent in quantum communication.

2.Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators

Authors:Yuichiro Mori, Kouhei Nakaji, Yuichiro Matsuzaki, Shiro Kawabata

Abstract: Quantum machine learning with variational quantum algorithms (VQA) has been actively investigated as a practical algorithm in the noisy intermediate-scale quantum (NISQ) era. Recent researches reveal that the data reuploading, which repeatedly encode classical data into quantum circuit, is necessary for obtaining the expressive quantum machine learning model in the conventional quantum computing architecture. However, the data reuploding tends to require large amount of quantum resources, which motivates us to find an alternative strategy for realizing the expressive quantum machine learning efficiently. In this paper, we propose quantum machine learning with Kerr-nonlinear Parametric Oscillators (KPOs), as another promising quantum computing device. The key idea is that we use not only the ground state and first excited state but also use higher excited states, which allows us to use a large Hilbert space even if we have a single KPO. Our numerical simulations show that the expressibility of our method with only one mode of the KPO is much higher than that of the conventional method with six qubits. Our results pave the way towards resource efficient quantum machine learning, which is essential for the practical applications in the NISQ era.

3.General Distance Balancing for Quantum Locally Testable Codes

Authors:Adam Wills, Ting-Chun Lin, Min-Hsiu Hsieh

Abstract: In this paper, we prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. arXiv:2004.07935 [quant-ph]. Our technical contribution is that the new soundness of the quantum code is at least the old soundness divided by the classical code length (up to a constant factor). This allows us to use any classical code with independent checks when distance balancing, where previously only the repetition code had been considered for qLTCs. By using a good classical LDPC code, we are able to grow the dimension of the hypersphere product codes arXiv:1608.05089 [quant-ph] and the hemicubic codes arXiv:1911.03069 [quant-ph] while maintaining their distance and locality, but at the expense of soundness. From this, and also by distance balancing a chain complex of Cross et al. arXiv:2209.11405 [cs.IT], we obtain quantum locally testable codes of new parameters.

4.Routing Protocols for Quantum Networks: Overview and Challenges

Authors:Binayak Kar, Pankaj Kumar

Abstract: Over the past 50 years, conventional network routing design has undergone substantial growth, evolving from small networks with static nodes to large systems connecting billions of devices. This progress has been achieved through the separation of concerns principle, which entails integrating network functionalities into a graph or random network design and employing specific network protocols to facilitate diverse communication capabilities. This paper aims to highlight the potential of designing routing techniques for quantum networks, which exhibit unique properties due to quantum mechanics. Quantum routing design requires a substantial deviation from conventional network design protocols since it must account for the unique features of quantum entanglement and information. However, implementing these techniques poses significant challenges, such as decoherence and noise in quantum systems, restricted communication ranges, and highly specialized hardware prerequisites. The paper commences by examining essential research on quantum routing design methods and proceeds to cover fundamental aspects of quantum routing, associated quantum operations, and the steps necessary for building efficient and robust quantum networks. This paper summarizes the present state of quantum routing techniques, including their principles, protocols, and challenges, highlighting potential applications and future directions.

5.Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

Authors:Sebastian Zielinski, Jonas Nüßlein, Jonas Stein, Thomas Gabor, Claudia Linnhoff-Popien, Sebastian Feld

Abstract: To solve 3SAT instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3SAT problem with regards to the solution quality on D-Wave's Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality.

6.Effect of depolarizing and quenching collisions on contrast of the coherent population trapping resonance

Authors:K. M. Sabakar, M. I. Vaskovskaya, D. S. Chuchelov, E. A. Tsygankov, V. V. Vassiliev, S. A. Zibrov, V. L. Velichansky

Abstract: We investigate the effect of buffer gases on the coherent population trapping resonance induced by a $\sigma$-polarized optical field in $^{87}$Rb atoms. Our experimental results show that inert gases, which depolarize the excited state of the alkali-metal atoms, provide higher contrast than nitrogen that effectively quenches their fluorescence. We also demonstrate that elimination of the spontaneous radiation does not significantly decrease the width at moderate temperatures of an atomic medium. Therefore, a mixture of inert gases can be preferable over a mixture with nitrogen for atomic clocks.

7.Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes

Authors:Dhruv Bhatnagar, Matthew Steinberg, David Elkouss, Carmen G. Almudever, Sebastian Feld

Abstract: Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit overhead, which is typically much smaller than in other approaches. However, as in most fault-tolerance protocols, the advantages of flag-style error correction come with a tradeoff: fault tolerance can be guaranteed, but such protocols involve high-depth circuits, due to the need for repeated stabilizer measurements. Here, we demonstrate that a dynamic choice of stabilizer measurements, based on past syndromes, and the utilization of elements from the full stabilizer group, leads to flag protocols with lower-depth syndrome-extraction circuits for the [[5,1,3]] code, as well as for the Steane code when compared to the standard methods in flag fault tolerance. We methodically prove that our new protocols yield fault-tolerant lookup tables, and demonstrate them with a pseudothreshold simulation, showcasing large improvements for all protocols when compared to previously-established methods. This work opens the dialogue on exploiting the properties of the full stabilizer group for reducing circuit overhead in fault-tolerant quantum-error correction.

8.Experimental Realization of Entangled Coherent States in Two-dimensional Harmonic Oscillators of a Trapped Ion

Authors:Honggi Jeon, Jiyong Kang, Jaeun Kim, Wonhyeong Choi, Kyunghye Kim, Taehyun Kim

Abstract: Entangled coherent states play pivotal roles in various fields such as quantum computation, quantum communication, and quantum sensing. We experimentally demonstrate the generation of entangled coherent states with the two-dimensional motion of a trapped ion system. Using Raman transitions with appropriate detunings, we simultaneously drive the red and blue sidebands of the two transverse axes of a single trapped ion and observe multi-periodic entanglement and disentanglement of its spin and two-dimensional motion. Then, by measuring the spin state, we herald entangled coherent states of the transverse motions of the trapped ion and observe the corresponding modulation in the parity of the phonon distribution of one of the harmonic oscillators. Lastly, we trap two ions in a linear chain and realize Molmer-Sorensen gate using two-dimensional motion.

9.Gaussian boson sampling with click-counting detectors

Authors:Gabriele Bressanini, Hyukjoon Kwon, M. S. Kim

Abstract: Gaussian boson sampling constitutes a prime candidate for an experimental demonstration of quantum advantage within reach with current technological capabilities. The original proposal employs photon-number-resolving detectors, however the latter are not widely available. On the other hand, inexpensive threshold detectors can be combined into a single click-counting detector to achieve approximate photon number resolution. We investigate the problem of sampling from a general multi-mode Gaussian state using click-counting detectors and show that the probability of obtaining a given outcome is related to a new matrix function which is dubbed as the Kensingtonian. We show how the latter relates to the Torontonian and the Hafnian, thus bridging the gap between known Gaussian boson sampling variants. We then prove that, under standard complexity-theoretical conjectures, the model can not be simulated efficiently.

10.Milestones on the Quantum Utility Highway

Authors:Catherine C. McGeoch, Pau Farre

Abstract: We introduce quantum utility, a new approach to evaluating quantum performance that aims to capture the user experience by including overhead costs associated with the quantum computation. A demonstration of quantum utility by a quantum processing unit (QPU) shows that the QPU can outperform classical solvers at some tasks of interest to practitioners, when considering computational overheads. We consider overhead costs that arise in standalone use of the QPU (as opposed to a hybrid computation context). We define three early milestones on the path to broad-scale quantum utility that focus on restricted subsets of overheads: Milestone 0 considers pure anneal time (no overheads) and has been demonstrated in previous work; Milestone 1 includes overhead times to access the QPU (that is, programming and readout); and Milestone 2 incorporates an indirect cost associated with minor embedding. We evaluate the performance of a D-Wave Advantage QPU with respect to Milestones 1 and 2, using a testbed of 13 input classes and seven classical solvers implemented on CPUs and GPUs. For Milestone 1, the QPU outperformed all classical solvers in 99% of our tests. For Milestone 2, the QPU outperformed all classical solvers in 19% of our tests, and the scenarios in which the QPU found success correspond to cases where classical solvers most frequently failed. Analysis of test results on specific inputs reveals fundamentally distinct underlying mechanisms that explain the observed differences in quantum and classical performance profiles. We present evidence-based arguments that these distinctions bode well for future annealing quantum processors to support demonstrations of quantum utility on ever-expanding classes of inputs and for more challenging milestones.

11.Search for dark photons with synchronized quantum sensor network

Authors:Min Jiang, Taizhou Hong, Dongdong Hu, Yifan Chen, Fengwei Yang, Tao Hu, Xiaodong Yang, Jing Shu, Yue Zhao, Xinhua Peng

Abstract: Ultralight dark photons constitute a well-motivated candidate for dark matter. Nevertheless, current constraints on the existence of dark photons with masses below MHz are predominantly set by cosmological or astrophysical limits. They behave as effective currents when coupled with standard model photons through kinetic mixing. When situated in electromagnetic shielded rooms, oscillating magnetic fields are generated with the maximum field strength proportional to the shield size. Here, we demonstrate a network of 15 atomic magnetometers, which are synchronized with the Global Positioning System (GPS) and are situated on the edges of two meter-scale shielded rooms, serving as a powerful tool to search for dark photons. Both the network multiple quantum sensors and the shield large size significantly enhance the expected dark-photon signals. Using this network, we constrain the kinetic mixing coefficient of dark photon dark matter over the mass range 1-500 Hz, which gives the strongest constraint of a terrestrial experiment within this mass window. Our prospect indicates that future data releases may go beyond the constraints from the Cosmic Microwave Background and the gas cloud cooling.

12.How the result of a measurement of a photon's mass can turn out to be 100

Authors:Yakov Bloch, Joshua Foo

Abstract: Bohmian mechanics has garnered significant attention as an interpretation of quantum theory since the paradigmatic experiments by Kocsis et. al. [Science 332, 6034 (2011)] and Mahler et. al. [Sci. Adv. 2, 2 (2016)], which inferred the average trajectories of photons in the nonrelativistic regime. These experiments were largely motivated by Wiseman's formulation of Bohmian mechanics, which grounded these trajectories in weak measurements. Recently, Wiseman's framework was extended to the relativistic regime by expressing the velocity field of single photons in terms of weak values of the photon energy and momentum. Here, we propose an operational, weak value-based definition for the Bohmian "local mass" of relativistic single particles. For relativistic wavefunctions satisfying the scalar Klein-Gordon equation, this mass coincides with the effective mass defined by de Broglie in his relativistic pilot-wave theory, a quantity closely connected with the quantum potential that is responsible for Bohmian trajectory self-bending and the anomalous photoelectric effect. We demonstrate the relationship between the photon trajectories and the mass in an interferometric setup.

13.Qubit readouts enabled by qubit cloaking

Authors:Manuel H. Muñoz-Arias, Cristóbal Lledó, Alexandre Blais

Abstract: Time-dependent drives play a crucial role in quantum computing efforts with circuit quantum electrodynamics. They enable single-qubit control, entangling logical operations, as well as qubit readout. However, their presence can lead to deleterious effects such as large ac-Stark shifts and unwanted qubit transitions ultimately reflected into reduced control or readout fidelities. Qubit cloaking was introduced in Lled\'o, Dassonneville, et al. [arXiv:2022.05758] to temporarily decouple the qubit from the coherent photon population of a driven cavity, allowing for the application of arbitrary displacements to the cavity field while avoiding the deleterious effects on the qubit. For qubit readout, cloaking permits to prearm the cavity with an, in principle, arbitrarily large number of photons, in anticipation to the qubit-state-dependent evolution of the cavity field, allowing for improved readout strategies. Here we take a closer look at two of them. First, arm-and-release readout, introduced together with qubit cloaking, where after arming the cavity the cloaking mechanism is released and the cavity field evolves under the application of a constant drive amplitude. Second, an arm-and-longitudinal readout scheme, where the cavity drive amplitude is slowly modulated after the release. We show that the two schemes complement each other, offering an improvement over the standard dispersive readout for any values of the dispersive interaction and cavity decay rate, as well as any target measurement integration time. Our results provide a recommendation for improving qubit readout without changes to the standard circuit QED architecture.

14.Reliable Quantum Communications based on Asymmetry in Purification and Coding

Authors:Lorenzo Valentini, René Bødker Christensen, Petar Popovski, Marco Chiani

Abstract: The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint on the latency of the quantum protocol, which brings the problem of quantum protocol design into the context of latency-reliability constraints. We address the problem through hybrid schemes that combine: (1) indirect transmission based on teleportation and purification; (2) direct transmission, based on quantum error correction (QEC). The intuition is that, at present, the quantum hardware offers low fidelity, which demands purification; on the other hand, low latency can be obtained by QEC techniques. It is shown that, in the proposed framework, the purification protocol gives rise to asymmetries that can be exploited by asymmetric quantum error correcting code (QECC), which sets the basis for unique hybrid purification and coding design. Our results show that ad-hoc asymmetric codes give, compared to conventional QEC, a performance boost and codeword size reduction both in a single link and in a quantum network scenario.

15.Nearly Heisenberg-limited noise-unbiased frequency estimation by tailored sensor design

Authors:Francisco Riberi, Gerardo Paz-Silva, Lorenza Viola

Abstract: We consider entanglement-assisted frequency estimation by Ramsey interferometry, in the presence of dephasing noise from spatiotemporally correlated environments.By working in the widely employed local estimation regime, we show that even for infinite measurement statistics, noise renders standard estimators biased or ill-defined. We introduce ratio estimators which, at the cost of doubling the required resources, are insensitive to noise and retain the asymptotic precision scaling of standard ones. While ratio estimators are applicable also in the limit of Markovian noise, we focus on non-Markovian dephasing from a bosonic bath and show how knowledge about the noise spectrum may be used to maximize metrological advantage, by tailoring the sensor's geometry. Notably, Heisenberg scaling is attained up to a logarithmic prefactor by maximally entangled states.

1.Unitary Averaging with Fault and Loss Tolerance

Authors:Ryan J. Marshman, Deepesh Singh, Austin P. Lund, Timothy C. Ralph

Abstract: We consider the impact of the unitary averaging framework on single and two-mode linear optical gates. We demonstrate that this allows a trade-off between the probability of success and gate fidelity, with perfect fidelity gates being achievable for a finite decrease in the probability of success, at least in principle. Furthermore, we show that the encoding and decoding errors in the averaging scheme can also be suppressed up to the first order. We also look at how unitary averaging can work in conjunction with existing error correction schemes. Specifically, we consider how parity encoding might be used to counter the extra loss due to the decreased probability of success, with the aim of achieving fault tolerance. We also consider how unitary averaging might be utilised to expand the parameter space in which fault tolerance may be achievable using standard fault tolerant schemes.

2.Entanglement of Magnetically Levitated Massive Schrödinger Cat States by Induced Dipole Interaction

Authors:Ryan J. Marshman, Sougato Bose, Andrew Geraci, Anupam Mazumdar

Abstract: Quantum entanglement provides a novel way to test short-distance quantum physics in a non-relativistic regime. We provide entanglement-based protocols to potentially test the magnetically induced dipole-dipole interaction and the Casimir-Polder potential between the two nano-crystals kept in a Schrodinger Cat state. Our scheme is based on the Stern-Gerlach (SG) apparatus, where we can witness the entanglement mediated by these interactions for the nano-crystal mass m~10^-19 kg with a spatial superposition size of order 0.1 micron in a trap relying on diamagnetic levitation. We show that it is possible to close the SG interferometer in position and momentum with a modest gradient in the magnetic field.

3.Robustness of controlled Hamiltonian approaches to unitary quantum gates

Authors:Eoin Carolan, Barış Çakmak, Steve Campbell

Abstract: We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyse their performance in terms of the gate infidelity, the associated resource overhead based on energetic cost, the susceptibility to time-keeping errors, and the degradation under environmental noise. Despite significant differences in the dynamical path taken, we find a broadly consistent behavior across the three approaches in terms of the efficacy of implementing the target gate and the resource overhead. Furthermore, we establish that the functional form of the control fields plays a crucial role in determining how faithfully a gate operation is achieved. Our results are demonstrated for single qubit gates, with particular focus on the Hadamard gate, and we discuss the extension to $N$-qubit operations.

4.Frequency tunable, cavity-enhanced single erbium quantum emitter in the telecom band

Authors:Yong Yu, Dorian Oser, Gaia Da Prato, Emanuele Urbinati, Javier Carrasco Ávila, Yu Zhang, Patrick Remy, Sara Marzban, Simon Gröblacher, Wolfgang Tittel

Abstract: Single quantum emitters embedded in solid-state hosts are an ideal platform for realizing quantum information processors and quantum network nodes. Among the currently-investigated candidates, Er$^{3+}$ ions are particularly appealing due to their 1.5 $\mu$m optical transition in the telecom band as well as their long spin coherence times. However, the long lifetimes of the excited state -- generally in excess of 1 ms -- along with the inhomogeneous broadening of the optical transition result in significant challenges. Photon emission rates are prohibitively small, and different emitters generally create photons with distinct spectra, thereby preventing multi-photon interference -- a requirement for building large-scale, multi-node quantum networks. Here we solve this challenge by demonstrating for the first time linear Stark tuning of the emission frequency of a single Er$^{3+}$ ion. Our ions are embedded in a lithium niobate crystal and couple evanescently to a silicon nano-photonic crystal cavity that provides an up to 143 increase of the measured decay rate. By applying an electric field along the crystal c-axis, we achieve a Stark tuning greater than the ion's linewidth without changing the single-photon emission statistics of the ion. These results are a key step towards rare earth ion-based quantum networks.

5.A massless interacting Fermionic Cellular Automaton exhibiting bound states

Authors:Edoardo Centofanti, Alessandro Bisio, Paolo Perinotti

Abstract: We present a Fermionic Cellular Automaton model which describes massless Dirac fermion in 1+1 dimension coupled with local, number preserving interaction. The diagonalization of the two particle sector shows that specific values of the total momentum and of the coupling constant allows for the formation of bound states.

6.Shallow-Depth Variational Quantum Hypothesis Testing

Authors:Mahadevan Subramanian, Sai Vinjanampathy

Abstract: The task of discriminating between two known quantum channels is a well known binary hypothesis testing task. We present a variational quantum algorithm with a parameterized state preparation and two-outcome positive operator valued measure (POVM) which defines the acceptance criteria for the hypothesis test. Both the state preparation and measurement are simultaneously optimized using success probability of single-shot discrimination as an objective function which can be calculated using localized measurements. Under constrained signal mode photon number quantum illumination we match the performance of known optimal 2-mode probes by simulating a bosonic circuit. Our results show that variational algorithms can prepare optimal states for binary hypothesis testing with resource constraints.

7.Giant-Atom Effects on Population and Entanglement Dynamics of Rydberg Atoms

Authors:Yao-Tong Chen, Lei Du, Yan Zhang, Lingzhen Guo, Jin-Hui Wu, M. Artoni, G. C. La Rocca

Abstract: Giant atoms are attracting interest as an emerging paradigm in the quantum optics of engineered waveguides. Here we propose to realize a synthetic giant atom working in the optical regime starting from a pair of interacting Rydberg atoms driven by a coherent field and coupled to a photonic crystal waveguide. Giant-atom effects can be observed as a phase-dependent decay of the double Rydberg excitation during the initial evolution of this atomic pair while (internal) atomic entanglement is exhibited at later times. Such an intriguing entanglement onset occurs in the presence of intrinsic atomic decay toward non-guided vacuum modes and is accompanied by an anti-bunching correlation of the emitted photons. Our findings may be relevant to quantum information processing, besides broadening the giant-atom waveguide physics with optically driven natural atoms.

8.Resonant generation of high-order harmonics in nonlinear electrodynamics

Authors:Ilia Kopchinskii, Petr Satunin

Abstract: We study the process of resonant generation of high-order harmonics in a closed cavity in the model of vacuum nonlinear electrodynamics. Concretely, we study the possibility of resonant generation of the third harmonic induced by a single electromagnetic mode in a radiofrequency cavity, as well as resonant generation of a combined frequency mode induced by two pump modes ($\omega_1$ and $\omega_2$). We explicitly show that the third harmonic as well as the $2\omega_1+\omega_2$ combined frequency mode are not resonantly amplified, while the $2\omega_1-\omega_2$ signal mode is amplified for certain cavity geometry. We discuss the process from the point of view of quantum theory.

9.Quantum enhanced non-interferometric quantitative phase imaging

Authors:Giuseppe Ortolano, Alberto Paniate, Pauline Boucher, Carmine Napoli, Sarika Soman, Silvania F. Pereira, Ivano Ruo Berchera, Marco Genovese

Abstract: Quantum entanglement and squeezing have significantly improved phase estimation and imaging in interferometric settings beyond the classical limits. However, for a wide class of non-interferometric phase imaging/retrieval methods vastly used in the classical domain e.g., ptychography and diffractive imaging, a demonstration of quantum advantage is still missing. Here, we fill this gap by exploiting entanglement to enhance imaging of a pure phase object in a non-interferometric setting, only measuring the phase effect on the free-propagating field. This method, based on the so-called "transport of intensity equation", is quantitative since it provides the absolute value of the phase without prior knowledge of the object and operates in wide-field mode, so it does not need time-consuming raster scanning. Moreover, it does not require spatial and temporal coherence of the incident light. Besides a general improvement of the image quality at a fixed number of photons irradiated through the object, resulting in better discrimination of small details, we demonstrate a clear reduction of the uncertainty in the quantitative phase estimation. Although we provide an experimental demonstration of a specific scheme in the visible spectrum, this research also paves the way for applications at different wavelengths, e.g., X-ray imaging, where reducing the photon dose is of utmost importance.

10.Gaussian eigenstate pinning in non-Hermitian quantum mechanics

Authors:Qi-Bo Zeng, Rong Lü

Abstract: We study the one-dimensional system subjected to a linearly varying imaginary vector potential, which is described by the single-particle continuous Schr\"odinger equation and is analytically solved. The eigenenergy spectrum is found to be real under open boundary condition (OBC) but forms a parabola in the complex energy plane under periodic boundary condition (PBC). The eigenstates always exhibit a modulated Gaussian distribution and are all pinned on the same position, which is determined by the imaginary vector potential and boundary conditions. These behaviors are in sharp contrast to the non-Hermitian skin effect (NHSE) in systems with constant imaginary vector potential, where the eigenstates are exponentially distributed under OBC but become extended under PBC. We further demonstrate that even though the spectrum under PBC is an open curve, the Gaussian type of NHSE still has a topological origin and is characterized by a nonvanishing winding number in the PBC spectrum. The energies interior to the parabola can support localized edge states under semi-infinite boundary condition. The corresponding tight-binding lattice models also show similar properties, except that the PBC spectrum form closed loops. Our work opens a door for the study of quantum systems with spatially varying imaginary vector potentials.

11.Ground state of composite bosons in low-dimensional graphs

Authors:Cecilia Cormick, Leonardo Ermann

Abstract: We consider a system of composite bosons given by strongly bound fermion pairs tunneling through sites that form a low-dimensional network. It has been shown that the ground state of this system can have condensate-like properties in the very dilute regime for two-dimensional lattices but displays fermionization for one-dimensional lattices. Studying graphs with fractal dimensions, we explore intermediate situations between these two cases and observe a correlation between increasing dimension and increasing condensate-like character. However, this is only the case for graphs for which the average path length grows with power smaller than 1 in the number of sites, and which have an unbounded circuit rank. We thus conjecture that these two conditions are relevant for condensation of composite bosons in arbitrary networks, and should be considered jointly with the well-established criterion of high entanglement between constituents.

12.Entanglement monogamy via multivariate trace inequalities

Authors:Mario Berta, Marco Tomamichel

Abstract: Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems. By combining these with multivariate matrix trace inequalities, we recover and sometimes strengthen various existing entanglement monogamy inequalities. In particular, we give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement by relating it to the relative entropy of entanglement measured with one-way local operations and classical communication, as well as for the faithfulness of conditional entanglement of mutual information by relating it to the separably measured relative entropy of entanglement. We discuss variations of these results using the relative entropy to states with positive partial transpose, and multipartite setups. Our results simplify and generalize previous derivations in the literature that employed operational arguments about the asymptotic achievability of information-theoretic tasks.

13.Wigner function dynamics with boundaries expressed as convolution

Authors:S. S. Seidov

Abstract: In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then generalized to the case of a particle confined in an infinite well in arbitrary dimensions. It is known, that boundary value problems in the phase space formulation of the quantum mechanics are surprisingly tricky. The complications arise from nonlocality of the expression involved in calculation of the Wigner function. Several ways of treating such problems were proposed. They are rather complicated and even exotic, involving, for example, corrections to the kinetic energy proportional to the derivatives of the Dirac delta--function. The presented in the manuscript approach is simpler both from analytical point of view and regarding numerical calculation. The solution is brought to a form of convolution of the free particle solution with some function, defined by the shape of the well. This procedure requires calculation of an integral, which can be done by developed analytical and numerical method.

14.Energy Cost of Localization of Relational Quantum Information

Authors:Adam Dukehart, David Mattingly

Abstract: Entanglement of spatially separated quantum states is usually defined with respect to a reference frame provided by some external observer. Thus, if one wishes to localize the quantum information within a spatially separated entangled state, one must enact an entanglement extraction protocol also defined with respect to that external frame. Entanglement extraction for Gaussian ground states in such an external frame construction has been shown to require a minimum energy and is hence an interesting process for gravitational physics, where examinations of localization vs. energy cost have a long history. General covariance however, precludes dependence on external frames. In order to enact an extraction protocol in a generally covariant theory, dependence on the external reference frame must first be removed and the states made relational. We examine the implementation of an extraction protocol for Gaussian states, who's center-of-mass and relational degrees of freedom are entangled, in a relational toy model where translation invariance stands in for full diffeomorphism invariance. Constructing fully relational states and the corresponding extraction/localization can, in principle, be done in two ways. External frame position information can be removed through $G$-twirling over translations or one can spontaneously break the translation symmetry via the gradient of an auxiliary field, or $Z$-model. We determine the energetics of quantum information localization after the states have been made fully relational via both the $G$-twirl and $Z$-model. We also show one can smoothly transition between the two approaches via positive operator valued measurements (POVM).

15.Excitons guided by polaritons

Authors:K. Mukherjee, S. Wüster

Abstract: We show that an exciton on a discrete chain of sites can be guided by effective measurements induced by an ambient, non-equilibrium medium that is synchronised to the exciton transport. For experimental verification, we propose a hybrid cold atom platform, carrying the exciton as electronic excitation on a chain of atoms, which are surrounded by a slow light medium supporting polaritons. The chain is coupled to the medium through long-range Rydberg interactions. Despite the guiding mechanism being incoherent, the exciton pulse can be coherently transported with high fidelity. The implementation requires careful alignment of chain and medium but then no further time-dependent control. Our concept can be ported to other exciton and polariton carrying media or devices, and will enable switches and waveguides operating with the two quasi particles involved, as we demonstrate.

16.Teleportation Revealed

Authors:Charles Alexandre Bédard

Abstract: Quantum teleportation is the name of a problem: how can the real-valued parameters encoding the state at Alice's location make their way to Bob's location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a conjuring trick. Investigating the phenomenon with Schr\"odinger states and reduced density matrices shall always leave loose ends because they are not local and complete descriptions of quantum systems. Upon demonstrating that the Heisenberg picture admits a local and complete description, Deutsch and Hayden rendered its explanatory power manifest by revealing the trick behind teleportation, namely, by providing an entirely local account. Their analysis is re-exposed and further developed.

17.A New Quantum Dempster Rule of Combination

Authors:Huaping He, Fuyuan Xiao

Abstract: Dempster rule of combination (DRC) is widely used for uncertainty reasoning in intelligent information system, which is generalized to complex domain recently. However, as the increase of identification framework elements, the computational complexity of Dempster Rule of Combination increases exponentially. To address this issue, we propose a novel quantum Dempster rule of combination (QDRC) by means of Toffoli gate. The QDRC combination process is completely implemented using quantum circuits.

18.Motional effects in dynamics of fluorescence of cold atomic ensembles excited by resonance pulse radiation

Authors:A. S. Kuraptsev, I. M. Sokolov

Abstract: We report the investigation of the influence of atomic motion on the fluorescence dynamics of dilute atomic ensemble driven by resonant pulse radiation. We show that even for sub-Doppler temperatures, the motion of atoms can significantly affect the nature of both superradiation and subradiation. We also demonstrate that, in the case of an ensemble of moving scatterers, it is possible to observe the nonmonotonic time dependence of the fluorescence rate. This leads to the fact that, in certain time intervals, increasing in temperature causes not an decrease but increase of the fluorescence intensity in the cone of coherent scattering. We have analyzed the role of the frequency diffusion of secondary radiation as a result of multiple light scattering in an optically dense medium. It is shown that spectrum broadening is the main factor which determines radiation trapping upon resonant excitation. At later time, after the trapping stage, the dynamics is dominated by close pairs of atoms (dimers). The dynamics of the excited states of these dimers has been studied in detail. It is shown that the change in the lifetime of the given adiabatic term of the diatomic quasi-molecule induced by the change in the interatomic distance as well as possible non-adiabatic transitions between sub- and superradiant states caused by atomic motion can lead not to the anticipated weakening of subradiation effect but to its enhancement.

19.Exact and approximate simulation of large quantum circuits on a single GPU

Authors:Daniel Strano, Benn Bollay, Aryan Blaauw, Nathan Shammah, William J. Zeng, Andrea Mari

Abstract: We benchmark the performances of Qrack, an open-source software library for the high-performance classical simulation of (gate-model) quantum computers. Qrack simulates, in the Schr\"odinger picture, the exact quantum state of $n$ qubits evolving under the application of a circuit composed of elementary quantum gates. Moreover, Qrack can also run approximate simulations in which a tunable reduction of the quantum state fidelity is traded for a significant reduction of the execution time and memory footprint. In this work, we give an overview of both simulation methods (exact and approximate), highlighting the main physics-based and software-based techniques. Moreover, we run computationally heavy benchmarks on a single GPU, executing large quantum Fourier transform circuits and large random circuits. Compared with other classical simulators, we report competitive execution times for the exact simulation of Fourier transform circuits with up to 27 qubits. We also demonstrate the approximate simulation of all amplitudes of random circuits acting on 54 qubits with 7 layers at average fidelity higher $\approx 4\%$, a task commonly considered hard without super-computing resources.

20.Quantum Fisher Information and its dynamical nature

Authors:Matteo Scandi, Paolo Abiuso, Jacopo Surace, Dario De Santis

Abstract: The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich range of possible quantum Fisher information, only a handful are typically used and studied. This review aims at collecting a number of results scattered in the literature that can be useful to people who begin the study of Fisher information and to those who are already working on it to have a more organic understanding of the topic. Moreover, we complement the review with new results about the relation between Fisher information and physical evolutions. Extending the study done in [1], we prove that all the physically realisable dynamics can be defined solely in terms of their relation with respect to the Fisher information metric. Moreover, other properties as Markovianity, retrodiction or detailed balance can be expressed in the same formalism. These results show a fact that was partially overseen in the literature, namely the inherently dynamical nature of Fisher information.

21.Zero noise extrapolation on logical qubits by scaling the error correction code distance

Authors:Misty A. Wahl, Andrea Mari, Nathan Shammah, William J. Zeng, Gokul Subramanian Ravi

Abstract: In this work, we migrate the quantum error mitigation technique of Zero-Noise Extrapolation (ZNE) to fault-tolerant quantum computing. We employ ZNE on \emph{logically encoded} qubits rather than \emph{physical} qubits. This approach will be useful in a regime where quantum error correction (QEC) is implementable but the number of qubits available for QEC is limited. Apart from illustrating the utility of a traditional ZNE approach (circuit-level unitary folding) for the QEC regime, we propose a novel noise scaling ZNE method specifically tailored to QEC: \emph{distance scaled ZNE (DS-ZNE)}. DS-ZNE scales the distance of the error correction code, and thereby the resulting logical error rate, and utilizes this code distance as the scaling `knob' for ZNE. Logical qubit error rates are scaled until the maximum achievable code distance for a fixed number of physical qubits, and lower error rates (i.e., effectively higher code distances) are achieved via extrapolation techniques migrated from traditional ZNE. Furthermore, to maximize physical qubit utilization over the ZNE experiments, logical executions at code distances lower than the maximum allowed by the physical qubits on the quantum device are parallelized to optimize device utilization. We validate our proposal with numerical simulation and confirm that ZNE lowers the logical error rates and increases the effective code distance beyond the physical capability of the quantum device. For instance, at a physical code distance of 11, the DS-ZNE effective code distance is 17, and at a physical code distance of 13, the DS-ZNE effective code distance is 21. When the proposed technique is compared against unitary folding ZNE under the constraint of a fixed number of executions of the quantum device, DS-ZNE outperforms unitary folding by up to 92\% in terms of the post-ZNE logical error rate.

1.Metrology in the Presence of Thermodynamically Consistent Measurements

Authors:Muthumanimaran Vetrivelan, Abhisek Panda, Sai Vinjanampathy

Abstract: Thermodynamically consistent measurements can either preserve statistics (unbiased) or preserve marginal states (non-invasive) but not both. Here we show the existence of metrological tasks which unequally favor each of the aforementioned measurement types. We consider two different metrology tasks, namely weak value amplification technique and repeated metrology without resetting. We observe that unbiased measurement is better than non-invasive measurement for the former and the converse is true for the latter. We provide finite temperature simulations of transmon sensors which estimate how much cooling, a resource for realistic measurements, is required to perform these metrology tasks.

2.On Kirkwood-Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame

Authors:Alexey E. Rastegin

Abstract: An issue which has attracted increasing attention in recent years are Kirkwood-Dirac quasiprobabilities. List of their use includes several questions of quantum information processing. Such quasiprobabilities naturally appear in the context of unravelings of a quantum channel. Complex tight frames also have potential applications in quantum information. Building principal Kraus operators of the frame vectors generates quasiprobabilities with interesting properties. For an equiangular tight frame, we characterize the Hilbert-Schmidt and spectral norms of the corresponding matrix. Hence, uncertainty relations are formulated in terms of R\'{e}nyi and Tsallis entropies. New inequalities for characterizing the location of eigenvalues are derived. They give an alternative to estimation on the base of Ger\v{s}gorin's theorem. The presented inequalities are exemplified with symmetric informationally complete measurement in dimension two.

3.Scalable quantum circuits for $n$-qubit unitary matrices

Authors:Rohit Sarma Sarkar, Bibhas Adhikari

Abstract: This work presents an optimization-based scalable quantum neural network framework for approximating $n$-qubit unitaries through generic parametric representation of unitaries, which are obtained as product of exponential of basis elements of a new basis that we propose as an alternative to Pauli string basis. We call this basis as the Standard Recursive Block Basis, which is constructed using a recursive method, and its elements are permutation-similar to block Hermitian unitary matrices.

4.A solid-state source of single and entangled photons at diamond SiV$^-$-center transitions operating at 80K

Authors:Xin Cao, Jingzhong Yang, Tom Fandrich, Yiteng Zhang, Eddy P. Rugeramigabo, Benedikt Brechtken, Rolf J. Haug, Michael Zopf, Fei Ding

Abstract: Large-scale quantum networks require the implementation of long-lived quantum memories as stationary nodes interacting with qubits of light. Epitaxially grown quantum dots hold great potential for the on-demand generation of single and entangled photons with high purity and indistinguishability. Coupling these emitters to memories with long coherence times enables the development of hybrid nanophotonic devices incorporating the advantages of both systems. Here we report the first GaAs/AlGaAs quantum dots grown by droplet etching and nanohole infilling method, emitting single photons with a narrow wavelength distribution (736.2 $\pm$ 1.7 nm) close to the zero-phonon line of Silicon-vacancy centers. Polarization entangled photons are generated via the biexciton-exciton cascade with a fidelity of (0.73 $\pm$ 0.09). High single photon purity is maintained from 4 K (g$^($$^2$$^)$(0) = 0.07 $\pm$ 0.02) up to 80 K (g$^($$^2$$^)$(0) = 0.11 $\pm$ 0.01), therefore making this hybrid system technologically attractive for real-world quantum photonic applications.

5.Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games

Authors:Minbo Gao, Zhengfeng Ji, Tongyang Li, Qisheng Wang

Abstract: We propose the first online quantum algorithm for zero-sum games with $\tilde O(1)$ regret under the game setting. Moreover, our quantum algorithm computes an $\varepsilon$-approximate Nash equilibrium of an $m \times n$ matrix zero-sum game in quantum time $\tilde O(\sqrt{m+n}/\varepsilon^{2.5})$, yielding a quadratic improvement over classical algorithms in terms of $m, n$. Our algorithm uses standard quantum inputs and generates classical outputs with succinct descriptions, facilitating end-to-end applications. As an application, we obtain a fast quantum linear programming solver. Technically, our online quantum algorithm "quantizes" classical algorithms based on the optimistic multiplicative weight update method. At the heart of our algorithm is a fast quantum multi-sampling procedure for the Gibbs sampling problem, which may be of independent interest.

6.Coherent and non-unitary errors in ZZ-generated gates

Authors:T. Mueller, T. Stollenwerk, D. Headley, M. Epping, F. K. Wilhelm

Abstract: Variational algorithms such as the Quantum Approximate Optimization Algorithm have attracted attention due to their potential for solving problems using near-term quantum computers. The $ZZ$ interaction typically generates the primitive two-qubit gate in such algorithms applied for a time, typically a variational parameter, $\gamma$. Different compilation techniques exist with respect to the implementation of two-qubit gates. Due to the importance of the $ZZ$-gate, we present an error analysis comparing the continuous-angle controlled phase gate (CP) against the fixed angle controlled $Z$-gate (CZ). We analyze both techniques under the influence of coherent over-rotation and depolarizing noise. We show that CP and CZ compilation techniques achieve comparable $ZZ$-gate fidelities if the incoherent error is below $0.03 \, \%$ and the coherent error is below $0.8 \, \%$. Thus, we argue that for small coherent and incoherent error a non-parameterized two-qubit gate such as CZ in combination with virtual $Z$ decomposition for single-qubit gates could lead to a significant reduction in the calibration required and, therefore, a less error-prone quantum device. We show that above a coherent error of $0.04 \pi$ ($2 \, \%$), the CZ gate fidelity depends significantly on $\gamma$.

7.Discrete frequency-bin entanglement generation via cascaded second-order nonlinear processes in Sagnac interferometer

Authors:Jiarui Li, Chenzhi Yuan, Si Shen, Zichang Zhang, Ruiming Zhang, Hao Li, You Wang, Guangwei Deng, Lixing You, Zhen Wang, Haizhi Song, Yunru Fan, Guangcan Guo, Qiang Zhou

Abstract: Discrete frequency-bin entanglement is an essential resource for applications in quantum information processing. In this Letter, we propose and demonstrate a scheme to generate discrete frequency-bin entanglement with a single piece of periodically poled lithium niobate waveguide in a modified Sagnac interferometer. Correlated two-photon states in both directions of the Sagnac interferometer are generated through cascaded second-order optical nonlinear processes. A relative phase difference between the two states is introduced by changing the polarization state of pump light, thus manipulating the two-photon state at the output of the Sagnac interferometer. The generated two-photon state is sent into a fiber polarization splitter, then a pure discrete frequency-bin entangled two-photon state is obtained by setting the pump light. The frequency entanglement property is measured by a spatial quantum beating with a visibility of $96.0 \pm 6.1\%$. The density matrix is further obtained with a fidelity of $98.0 \pm 3.0\%$ to the ideal state. Our demonstration provides a promising method for the generation of pure discrete frequency-bin entanglement at telecom band, which is desired in quantum photonics.

8.Full spatial characterization of entangled structured photons

Authors:Xiaoqin Gao, Yingwen Zhang, Alessio D'Errico, Alicia Sit, Khabat Heshami, Ebrahim Karimi

Abstract: Vector beams (VBs) are fully polarized beams with spatially varying polarization distributions, and they have found widespread use in numerous applications such as microscopy, metrology, optical trapping, nano-photonics, and communications. The entanglement of such beams has attracted significant interest, and it has been shown to have tremendous potential in expanding existing applications and enabling new ones. However, due to the complex spatially varying polarization structure of entangled VBs (EVBs), a complete entanglement characterization of these beams remains challenging and time-consuming. Here, we have used a time-tagging event camera to demonstrate the ability to simultaneously characterize approximately $2.6\times10^6$ modes between a bi-partite EVB using only 16 measurements. This achievement is an important milestone in high-dimensional entanglement characterization of structured light, and it could significantly impact the implementation of related quantum technologies. The potential applications of this technique are extensive, and it could pave the way for advancements in quantum communication, quantum imaging, and other areas where structured entangled photons play a crucial role.

9.Enhancing polarization transfer from nitrogen-vacancy centers in diamond to external nuclear spins via dangling bond mediators

Authors:H. Espinós, C. Munuera-Javaloy, I. Panadero, P. Acedo, R. Puebla, J. Casanova, E. Torrontegui

Abstract: The use of nitrogen-vacancy centers in diamond as a non-invasive platform for hyperpolarizing nuclear spins in molecular samples is a promising area of research with the potential to enhance the sensitivity of nuclear magnetic resonance experiments. Transferring NV polarization out of the diamond structure has been achieved on nanoscale targets using dynamical nuclear polarization methods, but extending this to relevant NMR volumes poses significant challenges. One major technical hurdle is the presence of paramagnetic defects in the diamond surface which can interfere with polarization outflow. However, these defects can also be harnessed as intermediaries for the interaction between NVs and nuclear spins. We present a method that benefits from existing microwave sequences, namely the PulsePol, to transfer polarization efficiently and robustly using dangling bonds or other localized electronic spins, with the potential to increase polarization rates under realistic conditions.

10.Estimating phase parameters of a three-level system interacting with two classical monochromatic fields in simultaneous and individual metrological strategies

Authors:Nour-Eddine Abouelkhir, Abdallah Slaoui, Hanane El Hadfi, Rachid Ahl Laamara

Abstract: Recently, the Hilbert-Schmidt speed, as a special class of quantum statistical speed, has been reported to improve the interferometric phase in single-parameter quantum estimation. Here, we test this concept in the multiparameter scenario where two laser phases are estimated in a theoretical model consisting of a three-level atom interacting with two classical monochromatic fields. When the atom is initially prepared in the lower bare state taking into account the detuning parameters, we extract an exact analytical solution of the atomic density matrix in the case of two-photon resonant transition. Further, we compare the performance of laser phase parameters estimation in individual and simultaneous metrological strategies, and we explore the role of quantum coherence in improving the efficiency of unknown multi-phase shift estimation protocols. The obtained results show that the Hilbert-Schmidt speed detects the lower bound on the statistical estimation error as well as the optimal estimation regions, where its maximal corresponds to the maximal quantum Fisher information, the performance of simultaneous multiparameter estimation with individual estimation inevitably depends on the detuning parameters of the three-level atom, and not only the quantum entanglement, but also the quantum coherence is a crucial resource to improve the accuracy of a metrological protocol.

11.Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus

Authors:Qiang Miao, Thomas Barthel

Abstract: We explain why and numerically confirm that there are no barren plateaus in the energy optimization of isometric tensor network states (TNS) for extensive Hamiltonians with finite-range interactions. Specifically, we consider matrix product states, tree tensor network states, and the multiscale entanglement renormalization ansatz. The variance of the energy gradient, evaluated by taking the Haar average over the TNS tensors, has a leading system-size independent term and decreases according to a power law in the bond dimension. For a hierarchical TNS with branching ratio $b$, the variance of the gradient with respect to a tensor in layer $\tau$ scales as $(b\eta)^\tau$, where $\eta$ is the second largest eigenvalue of the Haar-average doubled layer-transition channel and decreases algebraically with increasing bond dimension. The observed scaling properties of the gradient variance bear implications for efficient initialization procedures.

12.Finding, mapping and classifying optimal protocols for two-qubit entangling gates

Authors:Ignacio R. Sola, Seokmin Shin, Bo Y. Chang

Abstract: We characterize the set of optimal protocols for two-qubit entangling gates through a mechanism analysis based on quantum pathways, which allows us to compare and rank the different solutions. As an example of a flexible platform with a rich landscape of protocols, we consider trapped neutral atoms excited to Rydberg states by different pulse sequences that extend over several atomic sites, optimizing both the temporal and the spatial features of the pulses. Studying the rate of success of the algorithm under different constraints, we analyze the impact of the proximity of the atoms on the nature and quality of the optimal protocols. We characterize in detail the features of the solutions in parameter space, showing some striking correlations among the set of parameters. Together with the mechanism analysis, the spatio-temporal control allows us to select protocols that operate under mechanisms by design, like finding needles in the haystack.

13.Estimating the Energy Requirements to Operate a Cryptanalytically Relevant Quantum Computer

Authors:Edward Parker, Michael J. D. Vermeer

Abstract: The academic literature contains many estimates of the resources required to operate a cryptanalytically relevant quantum computer (CRQC) in terms of rather abstract quantities like the number of qubits. But to our knowledge, there have not been any estimates of these requirements in terms of more familiar economic resources like money or electricity. We demonstrate that the electrical energy required to break one cryptographic public key can be decomposed into the product of two factors. There is an extensive literature of previous estimates for one factor, the spacetime volume, that range over about six orders of magnitude; we discuss some interesting patterns in these estimates. We could not find any quantitative estimates at all for the other factor, the average power consumption per qubit. By combining several data points from existing superconducting-transmon quantum computers and extrapolating them to enormously larger scales, we make an extremely rough estimate of a plausible value of about six watts/qubit consumed by an eventual superconducting-transmon CRQC. By combining this estimate with a plausible spacetime volume estimate of $5.9 \times 10^6$ qubit-days from the prior literature, we estimate that - even after expending the enormous costs to build a CRQC - running it would require about 125 MW of electrical power, and using it to break one public key would cost about \$64,000 for electricity alone at current prices. Even if a CRQC is eventually built, merely operating it would probably remain the domain of nation-states and large organizations for a significant period of time.

14.Two-qubit atomic gates: Spatio-temporal control of Rydberg interaction

Authors:Ignacio R. Sola, Vladimir S. Malinovsky, Jaewook Ahn, Seokmin Shin, Bo Y. Chang

Abstract: By controlling the temporal and spatial features of light, we propose a novel protocol to prepare two-qubit entangling gates on atoms trapped at close distance, which could potentially speed up the operation of the gate from the sub-micro to the nanosecond scale. The protocol is robust to variations in the pulse areas and the position of the atoms, by virtue of the coherent properties of a dark state, which is used to drive the population through Rydberg states. From the time-domain perspective, the protocol generalizes the one proposed by Jaksch and coworkers [Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000)], with three pulses that operate symmetrically in time, but with different pulse areas. From the spatial-domain perspective, it uses structured light. We analyze the map of the gate fidelity, which forms rotated and distorted lattices in the solution space. Finally, we study the effect of an additional qubit to the gate performance and propose generalizations that operate with multi-pulse sequences.

15.Localization of quantum walk with classical randomness: Comparison between manual methods and supervised machine learning

Authors:Christopher Mastandrea, Chih-Chun Chien

Abstract: A transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceeds a critical value or the system size exceeds the localization length. We first establish the generality of the localization by showing its emergence in the presence of random rotation or translation. The transition point can be located manually by examining the probability distribution, momentum of inertia, and inverse participation ratio. As a comparison, we implement two supervised machine learning methods, the support vector machine and multi-layer perceptron neural network, with the same data. While both manual and machine-learning methods can identify the transition, the two machine-learning methods tend to underestimate the exponent of the localization length because of the fluctuating probability distribution. Our work illustrates challenges facing machine learning of physical systems with mixed quantum and classical probabilities.

16.Neutral Atom Quantum Computing Hardware: Performance and End-User Perspective

Authors:Karen Wintersperger, Florian Dommert, Thomas Ehmer, Andrey Hoursanov, Johannes Klepsch, Wolfgang Mauerer, Georg Reuber, Thomas Strohm, Ming Yin, Sebastian Luber

Abstract: We present an industrial end-user perspective on the current state of quantum computing hardware for one specific technological approach, the neutral atom platform. Our aim is to assist developers in understanding the impact of the specific properties of these devices on the effectiveness of algorithm execution. Based on discussions with different vendors and recent literature, we discuss the performance data of the neutral atom platform. Specifically, we focus on the physical qubit architecture, which affects state preparation, qubit-to-qubit connectivity, gate fidelities, native gate instruction set, and individual qubit stability. These factors determine both the quantum-part execution time and the end-to-end wall clock time relevant for end-users, but also the ability to perform fault-tolerant quantum computation in the future. We end with an overview of which applications have been shown to be well suited for the peculiar properties of neutral atom-based quantum computers.

17.Heisenberg Limit beyond Quantum Fisher Information

Authors:Wojciech Górecki

Abstract: The Heisenberg limit provides a fundamental bound on the achievable estimation precision with a limited number of $N$ resources used (e.g., atoms, photons, etc.). Using entangled quantum states makes it possible to scale the precision with $N$ better than when resources would be used independently. Consequently, the optimal use of all resources involves accumulating them in a single execution of the experiment. Unfortunately, that implies that the most common theoretical tool used to analyze metrological protocols - quantum Fisher information (QFI) - does not allow for a reliable description of this problem, as it becomes operationally meaningful only with multiple repetitions of the experiment. In this thesis, using the formalism of Bayesian estimation and the minimax estimator, I derive asymptotically saturable bounds on the precision of the estimation for the case of noiseless unitary evolution. For the case where the number of resources $N$ is strictly constrained, I show that the final measurement uncertainty is $\pi$ times larger than would be implied by a naive use of QFI. I also analyze the case where a constraint is imposed only on the average amount of resources, the exact value of which may fluctuate (in which case QFI does not provide any universal bound for precision). In both cases, I study the asymptotic saturability and the rate of convergence of these bounds. In the following part, I analyze the problem of the Heisenberg limit when multiple parameters are measured simultaneously on the same physical system. In particular, I investigate the existence of a gain from measuring all parameters simultaneously compared to distributing the same amount of resources to measure them independently. I focus on two examples - the measurement of multiple phase shifts in a multi-arm interferometer and the measurement of three magnetic field components.

18.Quantum signal processing with continuous variables

Authors:Zane M. Rossi, Victor M. Bastidas, William J. Munro, Isaac L. Chuang

Abstract: Quantum singular value transformation (QSVT) enables the application of polynomial functions to the singular values of near arbitrary linear operators embedded in unitary transforms, and has been used to unify, simplify, and improve most quantum algorithms. QSVT depends on precise results in representation theory, with the desired polynomial functions acting simultaneously within invariant two-dimensional subspaces of a larger Hilbert space. These two-dimensional transformations are largely determined by the related theory of quantum signal processing (QSP). While QSP appears to rely on properties specific to the compact Lie group SU(2), many other Lie groups appear naturally in physical systems relevant to quantum information. This work considers settings in which SU(1,1) describes system dynamics and finds that, surprisingly, despite the non-compactness of SU(1,1), one can recover a QSP-type ansatz, and show its ability to approximate near arbitrary polynomial transformations. We discuss various experimental uses of this construction, as well as prospects for expanded relevance of QSP-like ans\"atze to other Lie groups.

19.Semantic embedding for quantum algorithms

Authors:Zane M. Rossi, Isaac L. Chuang

Abstract: The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's realizing dynamics. As quantum computing matures, a similar need has developed for an assurance of the correctness of high-level quantum algorithmic reasoning. Parallel to this need, many quantum algorithms have been unified and improved using quantum signal processing (QSP) and quantum singular value transformation (QSVT), which characterize the ability, by alternating circuit ans\"atze, to transform the singular values of sub-blocks of unitary matrices by polynomial functions. However, while the algebraic manipulation of polynomials is simple (e.g., compositions and products), the QSP/QSVT circuits realizing analogous manipulations of their embedded polynomials are non-obvious. This work constructs and characterizes the runtime and expressivity of QSP/QSVT protocols where circuit manipulation maps naturally to the algebraic manipulation of functional transforms (termed semantic embedding). In this way, QSP/QSVT can be treated and combined modularly, purely in terms of the functional transforms they embed, with key guarantees on the computability and modularity of the realizing circuits. We also identify existing quantum algorithms whose use of semantic embedding is implicit, spanning from distributed search to proofs of soundness in quantum cryptography. The methods used, based in category theory, establish a theory of semantically embeddable quantum algorithms, and provide a new role for QSP/QSVT in reducing sophisticated algorithmic problems to simpler algebraic ones.

20.On the capacity of a quantum perceptron for storing biased patterns

Authors:Fabio Benatti, Giovanni Gramegna, Stefano Mancini, Gibbs Nwemadji

Abstract: Although different architectures of quantum perceptrons have been recently put forward, the capabilities of such quantum devices versus their classical counterparts remain debated. Here, we consider random patterns and targets independently distributed with biased probabilities and investigate the storage capacity of a continuous quantum perceptron model that admits a classical limit, thus facilitating the comparison of performances. Such a more general context extends a previous study of the quantum storage capacity where using statistical mechanics techniques in the limit of a large number of inputs, it was proved that no quantum advantages are to be expected concerning the storage properties. This outcome is due to the fuzziness inevitably introduced by the intrinsic stochasticity of quantum devices. We strengthen such an indication by showing that the possibility of indefinitely enhancing the storage capacity for highly correlated patterns, as it occurs in a classical setting, is instead prevented at the quantum level.

1.Recursive Quantum Eigenvalue/Singular-Value Transformation: Analytic Construction of Matrix Sign Function by Newton Iteration

Authors:Kaoru Mizuta, Keisuke Fujii

Abstract: Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant quantum algorithms such as Hamiltonian simulation. However, finding a parameter set which realizes preferable matrix functions in these techniques is difficult for large-scale quantum systems: there is no analytical result other than trivial cases as far as we know and we often suffer also from numerical instability. We propose recursive QET or QSVT (r-QET or r-QSVT), in which we can execute complicated matrix functions by recursively organizing block-encoding by low-degree QET or QSVT. Owing to the simplicity of recursive relations, it works only with a few parameters with exactly determining the parameters, while its iteration results in complicated matrix functions. In particular, by exploiting the recursive relation of Newton iteration, we construct the matrix sign function, which can be applied for eigenstate filtering for example, in a tractable way. We show that an analytically-obtained parameter set composed of only $8$ different values is sufficient for executing QET of the matrix sign function with an arbitrarily small error $\varepsilon$. Our protocol will serve as an alternative protocol for constructing QET or QSVT for some useful matrix functions without numerical instability.

2.A quantum fluctuation description of charge qubits

Authors:F. Benatti, F. Carollo, R. Floreanini, H. Narnhofer, F. Valiera

Abstract: We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction. Starting from the microscopic description of the latter in terms of two tunneling BCS models in the strong-coupling quasi-spin formulation, we derive the Hamiltonian governing the quantum behavior of the circuit in the limit of a large number $N$ of quasi-spins. Our approach relies on the identification of suitable quantum fluctuations, i.e. of collective quasi-spin operators, which account for the presence of fluctuation operators in the superconducting phase that retain a quantum character in spite of the large-$N$ limit. We show indeed that these collective quantum fluctuations generate the Heisenberg algebra on the circle and that their dynamics reproduces the one of the quantized charge-qubit, without the need of a phenomenological ``third quantization'' of a semiclassically inspired model. As a byproduct of our derivation, we explicitly obtain the temperature dependence of the junction critical Josephson current in the strong coupling regime, a result which is not directly accessible using standard approximation techniques.

3.Avoiding barren plateaus in the variational determination of geometric entanglement

Authors:Leonardo Zambrano, Andrés Damián Muñoz-Moller, Mario Muñoz, Luciano Pereira, Aldo Delgado

Abstract: The barren plateau phenomenon is one of the main obstacles to implementing variational quantum algorithms in the current generation of quantum processors. Here, we introduce a method capable of avoiding the barren plateau phenomenon in the variational determination of the geometric measure of entanglement for a large number of qubits. The method is based on measuring compatible two-qubit local functions whose optimization allows for achieving a well-suited initial condition, from which a global function can be further optimized without encountering a barren plateau. We analytically demonstrate that the local functions can be efficiently estimated and optimized. Numerical simulations up to 18-qubit GHZ and W states demonstrate that the method converges to the exact value. In particular, the method allows for escaping from barren plateaus induced by hardware noise or global functions defined on high-dimensional systems. Numerical simulations with noise are in agreement with experiments carried out on IBM's quantum processors for 7 qubits.

4.Mechanical cooling at the bistable regime of a dissipative optomechanical cavity with a Kerr medium

Authors:Ye Liu, Yang Liu, Chang-Sheng Hu, Yun-Kun Jiang, Huaizhi Wu, Yong Li

Abstract: In this paper, we study static bistability and mechanical cooling of a dissipative optomechanical cavity filled with a Kerr medium. The system exhibits optical bistability for a wide input-power range with the power threshold being greatly reduced, in contrast to the case of purely dissipative coupling. At the bistable regime, the membrane can be effectively cooled down to a few millikelvin from the room temperature under the unresolved sideband condition, where the effective mechanical temperature is a nonmonotonic function of intracavity intensity and reaches its minimum near the turning point of the upper stable branch. When the system is in the cryogenics environment, the effective mechanical temperature at the bistable regime shows a similar feature as in the room temperature case, but the optimal cooling appears at the monostable regime and approaches the mechanical ground state. Our results are of interest for further understanding bistable optomechanical systems, which have many applications in nonclassical state preparations and quantum information processing.

5.Post-processing noisy quantum computations utilizing N-representability constraints

Authors:Tomislav Piskor, Florian G. Eich, Michael Marthaler, Frank K. Wilhelm, Jan-Michael Reiner

Abstract: We propose and analyze a method for improving quantum chemical energy calculations on a quantum computer impaired by decoherence and shot noise. The error mitigation approach relies on the fact that the one- and two-particle reduced density matrices (1- and 2-RDM) of a chemical system need to obey so-called N-representability constraints. We post-process the result of an RDM measurement by projecting it into the subspace where certain N-representability conditions are fulfilled. Furthermore, we utilize that such constraints also hold in the hole and particle-hole sector and perform projections in these sectors as well. We expand earlier work by conducting a careful analysis of the method's performance in the context of quantum computing. Specifically, we consider typical decoherence channels (dephasing, damping, and depolarizing noise) as well as shot noise due to a finite number of projective measurements. We provide analytical considerations and examine numerically three example systems, \ch{H2}, \ch{LiH}, and \ch{BeH2}. From these investigations, we derive our own practical yet effective method to best employ the various projection options. Our results show the approach to significantly lower energy errors and measurement variances of (simulated) quantum computations.

6.Quantum-circuit algorithms for many-body topological invariant and Majorana zero mode

Authors:Takanori Sugimoto

Abstract: The topological state of matter is a potential resource to realize long-term fault-tolerant quantum computers beyond the near-term noisy intermediate-scale quantum devices. To achieve the realization, we need a deep understanding of topological behaviors in real quantum computers. However, quantum-circuit algorithms to analyze topological properties have still been insufficient. Here we propose three quantum-circuit algorithms, (i) to find the ground state in the selected parity subspace, (ii) to determine the many-body topological invariant, and (iii) to visualize the zero-energy edge mode. To demonstrate these algorithms, we adopt the interacting Kitaev chain as a typical model of many-body topological superconductors in one dimension. The algorithms are applicable to not only one-dimensional topological superconductors but other topological states including higher-dimensional systems.

7.Nonclassical photon-pair source based on noiseless photon echo

Authors:Duo-Lun Chen, Zong-Quan Zhou, Chuan-Feng Li, Guang-Can Guo

Abstract: The Duan-Lukin-Cirac-Zoller (DLCZ) scheme is a potential method to establish remote entanglements and realize large-scale quantum networks. Here we propose a DLCZ-like scheme based on the noiseless photon echo in rare-earth ion-doped crystals. Correlated photon pairs with a controllable delay can be created by the direct optical rephasing. Theoretical analysis indicates that the protocol is efficient in the low-optical-depth regime. This protocol could be feasibly implemented to establish long-lived quantum correlations between a photon and a spin-wave excitation in rare-earth ion-doped crystals.

8.Low-noise quantum frequency conversion in a monolithic bulk ppKTP cavity

Authors:Felix Mann, Felipe Gewers, Marlon Placke, Helen M. Chrzanowski, Sven Ramelow

Abstract: Interfacing the different building blocks of a future large scale quantum network will demand efficient and noiseless frequency conversion of quantum light. Nitrogen-vacancy (NV) centers in diamond are a leading candidate to form the nodes of such a network. However, the performance of a suitable converter remains a bottleneck, with existing demonstrations severely limited by parasitic noise arising at the target telecom wavelength. Here, we demonstrate a new platform for efficient low-noise quantum frequency conversion based on a monolithic bulk ppKTP cavity and show its suitability for the conversion of 637 nm single photons from NV centers in diamond to telecommunication wavelengths. By resonantly enhancing the power of an off-the-shelf pump laser, we achieve an internal conversion efficiency of $(72.3\pm 0.4)\%$ while generating only $(110\pm 4) \mbox{ kHz/nm}$ noise at the target wavelength without the need for any active stabilization. This constitutes a 5-fold improvement in noise over existing state-of-the-art single-step converters at this wavelengths. We verify the almost ideal preservation of non-classical correlations by converting photons from a spontaneous parametric down-conversion source and moreover show the preservation of time-energy entanglement via Franson interferometry.

9.Border Ranks of Positive and Invariant Tensor Decompositions: Applications to Correlations

Authors:Andreas Klingler, Tim Netzer, Gemma De les Coves

Abstract: The matrix rank and its positive versions are robust for small approximations, i.e. they do not decrease under small perturbations. In contrast, the multipartite tensor rank can collapse for arbitrarily small errors, i.e. there may be a gap between rank and border rank, leading to instabilities in the optimization over sets with fixed tensor rank. Can multipartite positive ranks also collapse for small perturbations? In this work, we prove that multipartite positive and invariant tensor decompositions exhibit gaps between rank and border rank, including tensor rank purifications and cyclic separable decompositions. We also prove a correspondence between positive decompositions and membership in certain sets of multipartite probability distributions, and leverage the gaps between rank and border rank to prove that these correlation sets are not closed. It follows that testing membership of probability distributions arising from resources like translational invariant Matrix Product States is impossible in finite time. Overall, this work sheds light on the instability of ranks and the unique behavior of bipartite systems.

10.Critical Cavity-Magnon Polariton Mediated Strong Long-Distance Spin-Spin Coupling

Authors:Miao Tian, Mingfeng Wang, Guo-Qiang Zhang, Hai-Chao Li, Wei Xiong

Abstract: Strong long-distance spin-spin coupling is desperately demanded for solid-state quantum information processing, but it is still challenged. Here, we propose a hybrid quantum system, consisting of a coplanar waveguide (CPW) resonator weakly coupled to a single nitrogen-vacancy spin in diamond and a yttrium-iron-garnet (YIG) nanosphere holding Kerr magnons, to realize strong long-distance spin-spin coupling. With a strong driving field on magnons, the Kerr effect can squeeze magnons, and thus exponentially enhance the coupling between the CPW resonator and the sequeezed magnons, which produces two cavity-magnon polaritons, i.e., the high-frequency polariton (HP) and low-frequency polariton (LP). When the enhanced cavity-magnon coupling approaches to the critical value, the spin is fully decoupled from the HP, while the coupling between the spin and the LP is significantly improved. In the dispersive regime, a strong spin-spin coupling is achieved with accessible parameters, and the coupling distance can be up to $\sim$cm. Our proposal provides a promising way to manipulate remote solid spins and perform quantum information processing in weakly coupled hybrid systems.

11.A no-broadcasting theorem for modal quantum theory

Authors:Phillip Diamond, Benjamin Schumacher, Michael D. Westmoreland

Abstract: The quantum no-broadcasting theorem has an analogue in modal quantum theory (MQT), a toy model based on finite fields. The failure of broadcasting in MQT is related to the failure of distributivity of the lattice of subspaces of the state space.

12.Quantum Natural Policy Gradients: Towards Sample-Efficient Reinforcement Lear