Quantum Physics (quant-ph)

Abstract: The success of a quantum algorithm hinges on the ability to orchestrate a successful application induction. Detrimental overheads in mapping general quantum circuits to physically implementable routines can be the deciding factor between a successful and erroneous circuit induction. In QASMTrans, we focus on the problem of rapid circuit transpilation. Transpilation plays a crucial role in converting high-level, machine-agnostic circuits into machine-specific circuits constrained by physical topology and supported gate sets. The efficiency of transpilation continues to be a substantial bottleneck, especially when dealing with larger circuits requiring high degrees of inter-qubit interaction. QASMTrans is a high-performance C++ quantum transpiler framework that demonstrates up to 369X speedups compared to the commonly used Qiskit transpiler. We observe speedups on large dense circuits such as uccsd_n24 and qft_n320 which require O(10^6) gates. QASMTrans successfully transpiles the aforementioned circuits in 69s and 31s, whilst Qiskit exceeded an hour of transpilation time. With QASMTrans providing transpiled circuits in a fraction of the time of prior transpilers, potential design space exploration, and heuristic-based transpiler design becomes substantially more tractable. QASMTrans is released at http://github.com/pnnl/qasmtrans.

Abstract: This article concerns the attraction domain analysis for steady states in Markovian open quantum systems. The central question is proposed as: given a steady state, which part of the state space of density operators does it attract and which part does it not attract? We answer this question by presenting necessary and sufficient conditions that determine, for any steady state and initial state, whether the latter belongs to the attraction domain of the former. Moreover, we show that steady states without uniqueness in the set of density operators have attraction domains with measure zero under some translation invariant and locally finite measures. Finally, an example regarding an open Heisenberg XXZ spin chain is presented.

Abstract: A $(K+1)-$plet of non-Hermitian and time-dependent operators (say, $\Lambda_j(t)$, $j=0,1,\ldots,K$) can be interpreted as the set of observables characterizing a unitary quantum system. What is required is the existence of a self-adjoint and, in general, time-dependent operator (say, $\Theta(t)$ called inner product metric) making the operators quasi-Hermitian, $\Lambda_j^\dagger(t)\Theta(t)=\Theta(t)\Lambda_j(t)$. The theory (called non-Hermitian interaction-picture, NIP) requires a separate description of the evolution of the states $\psi(t)$ (realized, via Schr\"{o}dinger-type equation, by a generator, say, $G(t)$) and of the observables themselves (a different generator (say, $\Sigma(t)(t)$) occurs in the related non-Hermitian Heisenberg-type equation). Every $\Lambda_j(t)$ (and, in particular, Hamiltonian $H(t)=\Lambda_0(t)$) appears isospectral to its hypothetical isospectral and self-adjoint (but, by assumption, prohibitively user-unfriendly) avatar $\lambda_j(t)=\Omega(t)\Lambda_j(t)\Omega^{-1}(t)$ with $\Omega^\dagger(t)\Omega(t)=\Theta(t)$. In our paper the key role played by identity $H(t)=G(t)+\Sigma(t)$ is shown to imply that there exist just three alternative meaningful implementations of the NIP approach, viz., ``number one'' (a ``dynamical'' strategy based on the knowledge of $H(t)$), ``number two'' (a ``kinematical'' one, based on the Coriolis force $\Sigma(t)$) and ``number three'' (in the literature, such a construction based on $G(t)$ is most popular but, paradoxically, it is also most complicated).

Abstract: The uncertainty principle lies at the heart of quantum mechanics, as it describes the fundamental trade-off between the precision of position and momentum measurements. In this work, we study the quantum particle in the Boltzmann states and derive a refined lower bound on the product of {\Delta}x and {\Delta}p. Our new bound is expressed in terms of the ratio between {\Delta}x and the thermal de Broglie wavelength, and provides a valuable tool for characterizing thermodynamic precision. We apply our results to the Brownian oscillator system, where we compare our new bound with the well-known Heisenberg uncertainty principle. Our analysis shows that our new bound offers a more precise measure of the thermodynamic limits of precision.

Abstract: We calculated the eigenvalues for a general N-channel coupled system with parity-time symmetry due to equal loss/gain. We found that the eigenspectrum displays a mixing of parity-time symmetric and broken phases, with N-2 of the eigenvalues being parity-time broken whereas the remaining two being either parity-time symmetric or broken depending on the loss/gain and coupling parameters. Our results also show that mixing of parity-time symmetric and parity-time broken phases can only be obtained for at least four-channels if other degrees of freedom like polarization is not taken into account.

Abstract: Up to now, experiments involving M\"ossbauer nuclei have been restricted to the low-excitation regime. The reason for this is the narrow spectral line width of the nuclei. This defining feature enables M\"ossbauer spectroscopy with remarkable resolution and convenient control and measurements in the time domain, but at the same time implies that only a tiny part of the photons delivered by accelerator-based x-ray sources with orders-of-magnitude larger pulse bandwidth are resonant with the nuclei. X-ray free-electron lasers promise a substantial enhancement of the number of nuclear-resonant photons per pulse, such that excitations beyond the low-excitation (LER) regime come within reach. This raises the question, how the onset of non-linear excitations could be experimentally verified. Here, we develop and explore a method to detect an excitation of nuclear ensembles beyond the LER for ensembles of nuclei embedded in x-ray waveguides. It relies on the comparison of the x-rays coherently and incoherently scattered off of the nuclei. As a key result, we show that the ratio of the two observables is constant within the LER, essentially independent of the details of the nuclear system and the characteristics of the exciting x-rays. Conversely, deviations from this equivalence serve as a direct indication of excitations beyond the LER. Building upon this observation, we develop a variety of experimental signatures both, for near-instantaneous impulsive and for temporally-extended non-impulsive x-ray excitation. Correlating coherently and incoherently scattered intensities further allows one to compare theoretical models of nonlinear excitations more rigorously to corresponding experiments.

Abstract: Current quantum computers have the potential to overcome classical computational methods, however, the capability of the algorithms that can be executed on noisy intermediate-scale quantum devices is limited due to hardware imperfections. Estimating the state of a qubit is often needed in different quantum protocols, due to the lack of direct measurements. In this paper, we consider the problem of estimating the quantum state of a qubit in a quantum processing unit without conducting direct measurements of it. We consider a parameterized measurement model to estimate the quantum state, represented as a quantum circuit, which is optimized using the quantum tomographic transfer function. We implement and test the circuit using the quantum computer of the Technical Research Centre of Finland as well as an IBM quantum computer. We demonstrate that the set of positive operator-valued measurements used for the estimation is symmetric and informationally complete. Moreover, the resources needed for qubit estimation are reduced when direct measurements are allowed, keeping the symmetric property of the measurements.

Abstract: Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals. This thesis discusses novel tools and techniques for the (classical) numerical modelling of quantum many-body wavefunctions exhibiting non-trivial correlations with the ultimate goal to introduce a universal framework for finding efficient quantum state representations. It is outlined how synergies with standard machine learning frameworks can be exploited to enable an automated inference of the relevant intrinsic characteristics, essentially without restricting the approximated state to specific (physically expected) correlation characteristics of the target. It is presented how rigorous Bayesian regression techniques, e.g. formalized via Gaussian Processes, can be utilized to introduce compact forms for various many-body states. Based on the probabilistic regression techniques forming the foundation of the resulting ansatz, coined the Gaussian Process State, different compression techniques are explored to efficiently extract a numerically feasible representation from which physical properties can be extracted. By following intuitively motivated modelling principles, the model carries a high degree of interpretability and offers an easily applicable tool for the study of different quantum systems, including ones inherently hard to simulate due to their strong correlation. This thesis outlines different perspectives on Gaussian Process States, and demonstrates the practical applicability of the numerical framework based on several benchmark applications, in particular, ground state approximations for prototypical quantum lattice models, Fermi-Hubbard models and $J_1-J_2$ models, as well as simple ab-initio quantum chemical systems.

Abstract: Trapped ions in radio-frequency traps are among the leading approaches for realizing quantum computers, due to high-fidelity quantum gates and long coherence times. However, the use of radio-frequencies presents a number of challenges to scaling, including requiring compatibility of chips with high voltages, managing power dissipation and restricting transport and placement of ions. By replacing the radio-frequency field with a 3 T magnetic field, we here realize a micro-fabricated Penning ion trap which removes these restrictions. We demonstrate full quantum control of an ion in this setting, as well as the ability to transport the ion arbitrarily in the trapping plane above the chip. This unique feature of the Penning micro-trap approach opens up a modification of the Quantum CCD architecture with improved connectivity and flexibility, facilitating the realization of large-scale trapped-ion quantum computing, quantum simulation and quantum sensing.

Abstract: In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure of entanglement. Additionally, we propose a novel approach to probe the underlying graph connectivity of genuine graph states, using quantum correlators of Pauli matrices. Our findings also reveal interesting implications for measurement processes, demonstrating the equivalence of certain projective measurements. Finally, we emphasize the simplicity of data analysis within this framework. This work contributes to a deeper understanding of the entanglement and connectivity properties of graph states, offering valuable insights for quantum information processing and quantum computing applications. In this work, we do not resort to the celebrated stabilizer formalism, which is the framework typically preferred for the study of this type of state; on the contrary, our approach is solely based on the concepts of expectation values, quantum correlations and projective measurement, which have the advantage of being very intuitive and fundamental tools of quantum theory.

Abstract: We introduce a new spin-squeezing technique that is a hybrid of two well established spin-squeezing techniques, quantum nondemolition measurement (QND) and one-axis twisting (OAT). This hybrid method aims to improve spin-squeezing over what is currently achievable using QND and OAT. In practical situations, the strength of both the QND and OAT interactions is limited. We found that in these situations, the hybrid scheme performed considerably better than either OAT or QND used in isolation. As QND and OAT have both been realised experimentally, this technique could be implemented in current atom interferometry setups with only minor modifications to the experiment.

Abstract: Quantum coherence is an indispensable resource for quantum technological applications. It is known to be distillable from a noisy form using operations that cannot create coherence. However, distillation exacts a hidden coherent measurement cost, whose extent has not previously been estimated. Here we show that this cost (quantified by an equivalent number of Hadamard measurements) is related to what we call the irretrievable coherence: the difference between the coherence of formation and the distillable coherence. We conjecture (and make partial progress towards proving) that when distilling from many copies of a given noisy coherent state, the coherent measurement cost scales extensively in the number of copies, at an asymptotic rate exactly equalling the input's irretrievable coherence. This cost applies to any application whereof coherence distillation is an incidental outcome (e.g. incoherent randomness extraction), but the implications are more dramatic if pure coherence is the only desired outcome: the measurement cost may often be higher than the distilled yield, in which case coherence should rather be prepared afresh than distilled from a noisy input.

Abstract: Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of the system. We show that already in the simplest possible scenarios it is possible to detect a definite, unbounded advantage of quantum systems over classical systems. We do this by constructing a family of operationally meaningful communication tasks each of which on one hand can be implemented by using just a single qubit but which on the other hand require unboundedly larger classical system for classical implementation. Furthemore, we show that even though with the additional resource of shared randomness the proposed communication tasks can be implemented by both quantum and classical systems of the same size, the number of coordinated actions needed for the classical implementation also grows unboundedly. In particular, no finite storage can be used to store all the coordinated actions needed to implement all the possible quantum communication tasks with classical systems. As a consequence, shared randomness cannot be viewed as a free resource.

Abstract: We frame entanglement detection as a problem of random variable inference to introduce a quantitative method to measure and understand whether entanglement witnesses lead to an efficient procedure for that task. Hence we quantify how many bits of information a family of entanglement witnesses can infer about the entanglement of a given quantum state sample. The bits are computed in terms of the mutual information and we unveil there exists hidden information not \emph{efficiently} processed. We show that there is more information in the expected value of the entanglement witnesses, i.e. $\mathbb{E}[W]=\langle W \rangle_\rho$ than in the sign of $\mathbb{E}[W]$. This suggests that an entanglement witness can provide more information about the entanglement if for our decision boundary we compute a different functional of its expectation value, rather than $\mathrm{sign}\left(\mathbb{E}\right [ W ])$.

Abstract: Atomic interferometers measure forces and acceleration with exceptional precision. The conventional approach to atomic interferometry is to launch an atomic cloud into a ballistic trajectory and perform the wave-packet splitting in momentum space by Raman transitions. This places severe constraints on the possible atomic trajectory, positioning accuracy and probing duration. Here, we propose and analyze a novel atomic interferometer that uses micro-optical traps (optical tweezers) to manipulate and control the motion of atoms. The new interferometer allows long probing time, sub micrometer positioning accuracy, and utmost flexibility in shaping of the atomic trajectory. The cornerstone of the tweezer interferometer are the coherent atomic splitting and combining schemes. We present two adiabatic schemes with two or three tweezers that are robust to experimental imperfections and work simultaneously with many vibrational states. The latter property allows for multi-atom interferometry in a single run. We also highlight the advantage of using fermionic atoms to obtain single-atom occupation of vibrational states and to eliminate mean-field shifts. We examine the impact of tweezer intensity noise and demonstrate that, when constrained by shot noise, the interferometer can achieve a relative accuracy better than $10^{-12}$ in measuring Earth's gravitational acceleration. The sub-micrometer resolution and extended measurement duration offer promising opportunities for exploring fundamental physical laws in new regimes. We discuss two applications well-suited for the unique capabilities of the tweezer interferometer: the measurement of gravitational forces and the study of Casimir-Polder forces between atoms and surfaces. Crucially, our proposed tweezer interferometer is within the reach of current technological capabilities.

Abstract: We provide a non-unit disk framework to solve combinatorial optimization problems such as Maximum Cut (Max-Cut) and Maximum Independent Set (MIS) on a Rydberg quantum annealer. Our setup consists of a many-body interacting Rydberg system where locally controllable light shifts are applied to individual qubits in order to map the graph problem onto the Ising spin model. Exploiting the flexibility that optical tweezers offer in terms of spatial arrangement, our numerical simulations implement the local-detuning protocol while globally driving the Rydberg annealer to the desired many-body ground state, which is also the solution to the optimization problem. Using optimal control methods, these solutions are obtained for prototype graphs with varying sizes at time scales well within the system lifetime and with approximation ratios close to one. The non-blockade approach facilitates the encoding of graph problems with specific topologies that can be realized in two-dimensional Rydberg configurations and is applicable to both unweighted as well as weighted graphs. A comparative analysis with fast simulated annealing is provided which highlights the advantages of our scheme in terms of system size, hardness of the graph, and the number of iterations required to converge to the solution.

Abstract: The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby integers whose prime factors are all small. This paper demonstrates that the hope of factoring numbers of commercial significance using these methods is unfounded. Mathematically, this is because the density of smooth numbers (numbers all of whose prime factors are small) decays exponentially as n grows. Our experimental reproductions and analysis show that lattice-based factoring does not scale successfully to larger numbers, that the proposed quantum enhancements do not alter this conclusion, and that other simpler classical optimization heuristics perform much better for lattice-based factoring. However, many topics in this area have interesting applications and mathematical challenges, independently of factoring itself. We consider particular cases of the CVP, and opportunities for applying quantum techniques to other parts of the factorization pipeline, including the solution of linear equations modulo 2. Though the goal of factoring 1000-bit numbers is still out-of-reach, the combinatoric landscape is promising, and warrants further research with more circumspect objectives.

Abstract: The First Passage Time (FPT) is the time taken for a stochastic process to reach a desired threshold. It finds wide application in various fields and has recently become particularly important in stochastic thermodynamics, due to its relation to kinetic uncertainty relations (KURs). In this letter we address the FPT of the stochastic measurement current in the case of continuously measured quantum systems. Our approach is based on a charge-resolved master equation, which is related to the Full-Counting statistics of charge detection. In the quantum jump unravelling we show that this takes the form of a coupled system of master equations, while for quantum diffusion it becomes a type of quantum Fokker-Planck equation. In both cases, we show that the FPT can be obtained by introducing absorbing boundary conditions, making their computation extremely efficient. The versatility of our framework is demonstrated with two relevant examples. First, we show how our method can be used to study the tightness of recently proposed KURs for quantum jumps. Second, we study the homodyne detection of a single two-level atom, and show how our approach can unveil various non-trivial features in the FPT distribution.

Abstract: Fault-tolerant complexes describe surface-code fault-tolerant protocols from a single geometric object. We first introduce fusion complexes that define a general family of fusion-based quantum computing (FBQC) fault-tolerant quantum protocols based on surface codes. We show that any 3-dimensional cell complex where each edge has four incident faces gives a valid fusion complex. This construction enables an automated search for fault tolerance schemes, allowing us to identify 627 examples within a moderate search time. We implement this using the open-source software tool Gavrog and present threshold results for a variety of schemes, finding fusion networks with higher erasure and Pauli thresholds than those existing in the literature. We then define more general structures we call fault-tolerant complexes that provide a homological description of fault tolerance from a large family of low-level error models, which include circuit-based computation, floquet-based computation, and FBQC with multi-qubit measurements. This extends the applicability of homological descriptions of fault tolerance, and enables the generation of many new schemes which have not been previously identified. We also define families of fault-tolerant complexes for color codes and 3d single-shot subsystem codes, which enables similar constructive methods, and we present several new examples of each.

Abstract: We perform theoretical calculations to investigate the naturally occurring high-frequency cutoff in a circuit comprising a flux qubit coupled inductively to a transmission line resonator (TLR). Our results agree with those of past studies that considered somewhat similar circuit designs. In particular, a decoupling occurs between the qubit and the high-frequency modes. As a result, the coupling strength between the qubit and resonator modes increases with mode frequency $\omega$ as $\sqrt{\omega}$ at low frequencies and decreases as $1/\sqrt{\omega}$ at high frequencies. We derive expressions for the multimode-resonator-induced Lamb shift in the qubit's characteristic frequency. Because of the natural decoupling between the qubit and high-frequency modes, the Lamb-shift-renormalized qubit frequency remains finite.

Abstract: We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network architecture, and is motivated by the correlation structure inherent in the data, as well as any relevant compositional structure, resulting in tree-like connectivity. Our models are specifically constructed using parameterised quantum circuits, widely used in quantum machine learning, effectively using Hilbert space as a feature space. Furthermore, they are efficiently trainable due to their tree-like structure. We demonstrate experimental results for the task of binary classification of sequences from real-world datasets relevant to natural language and bioinformatics, characterised by long-range correlations and often equipped with syntactic information. Since our models have a valid operational interpretation as quantum processes, we also demonstrate their implementation on Quantinuum's H2-1 trapped-ion quantum processor, demonstrating the possibility of efficient sequence processing on near-term quantum devices. This work constitutes the first scalable implementation of near-term quantum language processing, providing the tools for large-scale experimentation on the role of tensor structure and syntactic priors. Finally, this work lays the groundwork for generative sequence modelling in a hybrid pipeline where the training may be conducted efficiently in simulation, while sampling from learned probability distributions may be done with polynomial speed-up on quantum devices.

Abstract: In device-independent cryptography, it is known that reuse of devices across multiple protocol instances can introduce a vulnerability against memory attacks. This is an introductory note to highlight that even if we restrict ourselves to device-dependent QKD and only consider a single protocol instance, memory effects across rounds are enough to cause substantial difficulties in applying many existing non-IID proof techniques, such as de Finetti reductions and complementarity-based arguments (e.g. analysis of phase errors). We present a quick discussion of these issues, including some tailored scenarios where protocols admitting security proofs via those techniques become insecure when memory effects are allowed, and we highlight connections to recently discussed attacks on DIQKD protocols that have public announcements based on the measurement outcomes. This discussion indicates the challenges that would need to be addressed in order to apply those techniques in the presence of memory effects (for either the device-dependent or device-independent case), even for a single protocol instance.

Abstract: This study explores the transfer of nonclassical correlations from an ultra-cold atom system to a pair of pulsed laser beams. Through nondestructive local probe measurements, we introduce an alternative to destructive techniques for mapping BEC entanglement. Operating at ultralow temperatures, the setup emulates a relativistic vacuum field, using lasers as Unruh-DeWitt detectors for phonons. The vacuum holds intrinsic entanglement, transferable to distant probes briefly interacting with it - a phenomenon termed ``entanglement harvesting''. Our study accomplishes two primary objectives: first, establishing a mathematical equivalence between a pair of pulsed laser probes interacting with an effective relativistic field and the entanglement harvesting protocol; and second, to closely examine the potential and persisting obstacles for realising this protocol in an ultra-cold atom experiment.

Abstract: We investigate a ring cavity comprising two degenerate counter-propagating modes coupled to a one-dimensional atomic chain, leading to bidirectional light scattering. The spatial configuration of the atomic chain, described by a structure factor, plays a crucial role in manipulation of the atom-cavity interactions and formation of the collective excitation modes. Remarkably, we observe that a cavity dark mode is induced when the atomic spacing is an integer multiple of half-wavelength. The nodes of this standing-wave dark mode align precisely with the atomic positions, enabling intracavity field conversion without free space scattering. By adjusting the configuration of the atomic chain, we realize optical mode conversion with almost no photon loss and a broad tuning range, making it suitable for various practical applications in quantum technologies.

Abstract: Quantum systems have entered a competitive regime where classical computers must make approximations to represent highly entangled quantum states. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices, and it remains unsolved how to estimate the actual entanglement content of experiments. Here we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analog Rydberg quantum simulator, reaching a high entanglement entropy regime where exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against many approximate classical algorithms with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only one, which we introduce here, is able to keep pace with the experiment on the classical hardware we employ. Our results enable a new paradigm for evaluating the performance of both analog and digital quantum devices in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

Abstract: Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and a decoding algorithm. Here we present an end-to-end quantum error correction protocol that implements fault-tolerant memory based on a family of LDPC codes with a high encoding rate that achieves an error threshold of $0.8\%$ for the standard circuit-based noise model. This is on par with the surface code which has remained an uncontested leader in terms of its high error threshold for nearly 20 years. The full syndrome measurement cycle for a length-$n$ code in our family requires $n$ ancillary qubits and a depth-7 circuit composed of nearest-neighbor CNOT gates. The required qubit connectivity is a degree-6 graph that consists of two edge-disjoint planar subgraphs. As a concrete example, we show that 12 logical qubits can be preserved for ten million syndrome cycles using 288 physical qubits in total, assuming the physical error rate of $0.1\%$. We argue that achieving the same level of error suppression on 12 logical qubits with the surface code would require more than 4000 physical qubits. Our findings bring demonstrations of a low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.