Quantum Physics (quant-ph)

Abstract: In this article, we pedagogically revisit the Stark effect of hydrogen atom induced by a uniform static electric field. In particular, a general formula for the integral of associated Laguerre polynomials was derived by applying the method for Hermite polynomials of degree n proposed in the work [Anh-Tai T.D. et al., 2021 AIP Advances \textbf{11} 085310]. The quadratic Stark effect is obtained by applying this formula and the time-independent non-degenerate perturbation theory to hydrogen. Using the Siegert State method, numerical calculations are performed and serve as data for benchmarking. The comparisons are then illustrated for the ground state and some highly excited states of hydrogen to provide an insightful look at the applicable limit and precision of the quadratic Stark effect formula for other atoms with comparable properties.

Abstract: We report on a method to certify a unitary operation with the help of source and measurement apparatuses whose calibration throughout the certification process needs not be trusted. As in the device-independent paradigm our certification method relies on a Bell test, but it removes the need for high detection efficiencies by including the single additional assumption that non-detected events are independent of the measurement settings. The relevance of the proposed method is demonstrated experimentally with the certification of a quantum frequency converter. The experiment starts with the heralded creation of a maximally entangled two-qubit state between a single $^{40}$Ca$^+$ ion and a 854$\,$nm photon. Entanglement preserving frequency conversion to the telecom band is then realized with a non-linear waveguide embedded in a Sagnac interferometer. The resulting ion-telecom photon entangled state is characterized by means of a Bell-CHSH test from which the quality of the frequency conversion is quantified. We demonstrate the successful frequency conversion with an average certified fidelity of $\geq 84\,\%$ and an efficiency $\geq 3.1\times 10^{-6}$ at a confidence level of $99\,\%$. This ensures the suitability of the converter for integration in quantum networks from a trustful characterization procedure.

Abstract: In this paper we aim to push the analogy between thermodynamics and quantum resource theories one step further. Previous inspirations were based on thermodynamic considerations concerning scenarios with a single heat bath, neglecting an important part of thermodynamics that studies heat engines operating between two baths at different temperatures. Here, we investigate the performance of resource engines, which replace the access to two heat baths at different temperatures with two arbitrary constraints on state transformations. The idea is to imitate the action of a two--stroke heat engine, where the system is sent to two agents (Alice and Bob) in turns, and they can transform it using their constrained sets of free operations. We raise and address several questions, including whether or not a resource engine can generate a full set of quantum operations or all possible state transformations, and how many strokes are needed for that. We also explain how the resource engine picture provides a natural way to fuse two or more resource theories, and we discuss in detail the fusion of two resource theories of thermodynamics with two different temperatures, and two resource theories of coherence with respect to two different bases.

Abstract: Collective coupling of an ensemble of particles to a light field is commonly described by the Tavis--Cummings model. This model includes numerous eigenstates which are optically decoupled from the optically bright polariton states. To access these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in molecular Tavis--Cummings model. The system is modelled with a Lindblad equation that includes pure dephasing, as they would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of the pure dephasing, as well as the number of particles, has a significant influence on the dark state population.

Abstract: Quantum transmission links are central elements in essentially all implementations of quantum information protocols. Emerging progress in quantum technologies involving such links needs to be accompanied by appropriate certification tools. In adversarial scenarios, a certification method can be vulnerable to attacks if too much trust is placed on the underlying system. Here, we propose a protocol in a device independent framework, which allows for the certification of practical quantum transmission links in scenarios where minimal assumptions are made about the functioning of the certification setup. In particular, we take unavoidable transmission losses into account by modeling the link as a completely-positive trace-decreasing map. We also, crucially, remove the assumption of independent and identically distributed samples, which is known to be incompatible with adversarial settings. Finally, in view of the use of the certified transmitted states for follow-up applications, our protocol moves beyond certification of the channel to allow us to estimate the quality of the transmitted state itself. To illustrate the practical relevance and the feasibility of our protocol with currently available technology we provide an experimental implementation based on a state-of-the-art polarization entangled photon pair source in a Sagnac configuration and analyze its robustness for realistic losses and errors.

Abstract: Mode-pairing (MP) quantum key distribution (QKD) eliminates the requirements of phase locking and phase tracking compared with twin-field (TF) QKD while still surpassing the fundamental rate-distance limit of QKD. The complexity of the experimental implementation is reduced while the efficiency is also guaranteed. The security of MP-QKD is proved rigorously by examining the consistency of the states detailly between MP-QKD and the fixed-pairing scheme under all of Eve's possible interference, where the latter is equivalent to measurement-device-independent (MDI) QKD. Here we propose a simple and straightforward method to prove the information-theoretic security of MP-QKD. Specifically, an entanglement scheme for MP-QKD is proposed and its security is proved using entanglement purification. Then the security of MP-QKD can be guaranteed with the equivalence of the entanglement scheme and prepare-and-measure scheme for MP-QKD. With this approach, it is beneficial to analyze and understand the performance and security of MP-QKD. We explain why the pairing rounds in MP-QKD can be decoupled and determined by the measurement results announced by a third party, which is the key difference between MP-QKD and MDI-QKD. Moreover, we analyze the security of MP-QKD with the allowed optimal pairing strategy, which is significant for the secret key rate, under collective and coherent attacks.

Abstract: We report a design and implementation of a resource-efficient spatial demultiplexer which produces 4 indistinguishable photons with efficiency of 39.7% per channel. Our scheme is based on a free-space storage/delay line which accumulates 4 photons and releases them by a controlled polarization rotation using a single Pockels cell.

Abstract: Many relevant problems in industrial settings result in NP-hard optimization problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP). Even with today's most powerful classical algorithms, the CVRP is challenging to solve classically. Quantum computing may offer a way to improve the time to solution, although the question remains open as to whether Noisy Intermediate-Scale Quantum (NISQ) devices can achieve a practical advantage compared to classical heuristics. The most prominent algorithms proposed to solve combinatorial optimization problems in the NISQ era are the Quantum Approximate Optimization Algorithm (QAOA) and the more general Variational Quantum Eigensolver (VQE). However, implementing them in a way that reliably provides high-quality solutions is challenging, even for toy examples. In this work, we discuss decomposition and formulation aspects of the CVRP and propose an application-driven way to measure solution quality. Considering current hardware constraints, we reduce the CVRP to a clustering phase and a set of TSPs. For the TSP, we extensively test both QAOA and VQE and investigate the influence of various hyperparameters, such as the classical optimizer choice and strength of constraint penalization. Results of QAOA are generally of limited quality because the algorithm does not reach the energy threshold for feasible TSP solutions, even when considering various extensions such as recursive, warm-start and constraint-preserving mixer QAOA. On the other hand, the VQE reaches the energy threshold and shows a better performance. Our work outlines the obstacles to quantum-assisted solutions for real-world optimization problems and proposes perspectives on how to overcome them.

Abstract: We relate the probability distribution of the work done on a statistical system under a sudden quench to the Lanczos coefficients corresponding to evolution under the post-quench Hamiltonian. Using the general relation between the moments and the cumulants of the probability distribution, we show that the Lanczos coefficients can be identified with physical quantities associated with the distribution, e.g., the average work done on the system, its variance, as well as the higher order cumulants. In a sense this gives an interpretation of the Lanczos coefficients in terms of experimentally measurable quantities. We illustrate these relations with two examples. The first one involves quench done on a harmonic chain with periodic boundary conditions and with nearest neighbour interactions. As a second example, we consider mass quench in a free bosonic field theory in $d$ spatial dimensions in the limit of large system size. In both cases, we find out the time evolution of the spread complexity after the quench, and relate the Lanczos coefficients with the cumulants of the distribution of the work done on the system.

Abstract: We investigate the steady-state phase transitions in an all-to-all transverse-field Ising model subjected to an environment. The considered model is composed of two ingredient Hamiltonians. The orientation of the external field, which is perpendicular to the spin interaction, can be tuned to be along either $x$-direction or $z$-direction in each ingredient Hamiltonian while the dissipations always tend to flip the spins down to the $z$-direction. By means of mean-field approximation, we find that the quasi continuous steady-state phase transition is presented as a consequence of the merging of two branches of steady-state solutions. The emergence of bistability is confirmed by analyzing the steady-state behaviors of a set of finite-size systems which is also revealed by the Liouvillian spectrum.

Abstract: The extraction of randomness from weakly random seeds is a problem of central importance with multiple applications. In the device-independent setting, this problem of quantum randomness amplification has been mainly restricted to specific weak sources of Santha-Vazirani type, while extraction from the general min-entropy sources has required a large number of separated devices which is impractical. In this paper, we present a device-independent protocol for amplification of a single min-entropy source (consisting of two blocks of sufficiently high min-entropy) using a device consisting of two spatially separated components and show a proof of its security against general quantum adversaries.

Abstract: This paper presents a new `partitional' approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM. Since at the set level, partitions are the mathematical tool to represent distinctions and indistinctions (or definiteness and indefiniteness), this approach shows how to interpret the key non-classical QM notion of superposition in terms of (objective) indefiniteness between definite alternatives (as opposed to seeing it as the sum of `waves'). Hence this partitional approach substantiates what might be called the Objective Indefiniteness Interpretation or what Abner Shimony called the Literal Interpretation of QM.

Abstract: This paper introduces the QDQN-DPER framework to enhance the efficiency of quantum reinforcement learning (QRL) in solving sequential decision tasks. The framework incorporates prioritized experience replay and asynchronous training into the training algorithm to reduce the high sampling complexities. Numerical simulations demonstrate that QDQN-DPER outperforms the baseline distributed quantum Q learning with the same model architecture. The proposed framework holds potential for more complex tasks while maintaining training efficiency.

Abstract: We propose a model-based reinforcement learning (RL) approach for noisy time-dependent gate optimization with improved sample complexity over model-free RL. Sample complexity is the number of controller interactions with the physical system. Leveraging an inductive bias, inspired by recent advances in neural ordinary differential equations (ODEs), we use an auto-differentiable ODE parametrised by a learnable Hamiltonian ansatz to represent the model approximating the environment whose time-dependent part, including the control, is fully known. Control alongside Hamiltonian learning of continuous time-independent parameters is addressed through interactions with the system. We demonstrate an order of magnitude advantage in the sample complexity of our method over standard model-free RL in preparing some standard unitary gates with closed and open system dynamics, in realistic numerical experiments incorporating single shot measurements, arbitrary Hilbert space truncations and uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be leveraged by existing control methods like GRAPE for further gradient-based optimization with the controllers found by RL as initializations. Our algorithm that we apply on nitrogen vacancy (NV) centers and transmons in this paper is well suited for controlling partially characterised one and two qubit systems.

Abstract: We theoretically and computationally investigate the behavior of infinite atom arrays when illuminated by nearly resonant light. We use higher order mean field equations to investigate the coherent reflection and transmission and incoherent scattering of photons from a single array and from a pair of arrays as a function of detuning for different values of the Rabi frequency. For the single array case, we show how increasing the light intensity changes the probabilities for these different processes. For example, the incoherent scattering probability initially increases with light intensity before decreasing at higher values. For a pair of parallel arrays at near resonant separation, the effects from increasing light intensity can become apparent with incredibly low intensity light. In addition, we derive the higher order mean field equations for these infinite arrays giving a representation that can be evaluated with a finite number of equations.

Abstract: Spin-glass (SG) is a fascinating system that has garnered significant attention due to its intriguing properties and implications for various research fields. One of the key characteristics of spin glasses is that they contain random disorder, which leads to many possible states of the system occurring with very close probabilities. We explore the concept of spin-glass superposition states (SSs), which are equiprobable SSs of possible electronic configurations. Using the Edward-Anderson (EA) type SG order parameter $q_{EA}$ and magnetization, we demonstrate that these SSs can be classified based on their contribution to distinguishing magnetic order (disorder), such as SG, (anti)ferromagnetic (FM), and paramagnetic (PM) phases. We also generalize these superposition states based on the system size and investigate the entanglement of these phase-based SSs using the negativity measure. We show that the SG order parameter can be utilized to determine the entanglement of magnetically ordered (disordered) phases, or vice versa, with negativity signifying magnetic order. Our findings provide further insight into the nature of quantum SSs and their relevance to SGs and quantum magnets. They have implications for various fields, including condensed matter physics, where SGs are a prototypical example of disordered systems. They are also relevant for other fields, such as neural networks, optimization problems, and information storage, where complex systems with random disorder behavior are greatly interested. Overall, our study provides a deeper understanding of the behavior of SGs and the nature of quantum SSs, with potential applications in various fields.

Abstract: A Zero-Knowledge Protocol (ZKP) allows one party to convince another party of a fact without disclosing any extra knowledge except the validity of the fact. For example, it could be used to allow a customer to prove their identity to a potentially malicious bank machine without giving away private information such as a personal identification number. This way, any knowledge gained by a malicious bank machine during an interaction cannot be used later to compromise the client's banking account. An important tool in many ZKPs is bit commitment, which is essentially a digital way for a sender to put a message in a lock-box, lock it, and send it to the receiver. Later, the key is sent for the receiver to open the lock box and read the message. This way, the message is hidden from the receiver until they receive the key, and the sender is unable to change their mind after sending the lock box. In this paper, the homomorphic properties of a particular multi-party commitment scheme are exploited to allow the receiver to perform operations on commitments, resulting in polynomial time ZKPs for two NP-Complete problems: the Subset Sum Problem and 3SAT. These ZKPs are secure with no computational restrictions on the provers, even with shared quantum entanglement. In terms of efficiency, the Subset Sum ZKP is competitive with other practical quantum-secure ZKPs in the literature, with less rounds required, and fewer computations.

Abstract: A major thrust in quantum algorithm development over the past decade has been the search for the quantum algorithms that will deliver practical quantum advantage first. Today's quantum computers and even early fault-tolerant quantum computers will be limited in the number of operations they can implement per circuit. We introduce quantum algorithms for ground state energy estimation (GSEE) that accommodate this design constraint. The first estimates ground state energies and has a quadratic improvement on the ground state overlap parameter compared to other methods in this regime. The second certifies that the estimated ground state energy is within a specified error tolerance of the true ground state energy, addressing the issue of gap estimation that beleaguers several ground state preparation and energy estimation algorithms. We note, however, that the scaling of this certification technique is, unfortunately, worse than that of the GSEE algorithm. These algorithms are based on a novel use of the quantum computer to facilitate rejection sampling. After a classical computer is used to draw samples, the quantum computer is used to accept or reject the samples. The set of accepted samples correspond to draws from a target distribution. While we use this technique for ground state energy estimation, it may find broader application. Our work pushes the boundaries of what operation-limited quantum computers are capable of and thus brings the target of quantum advantage closer to the present.

Abstract: In a fast scrambling many-body quantum system, information is spread and entanglement is built up on a timescale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error correcting codes. In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a transition point between two clearly defined regimes of different dynamical behaviour. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic, sparse circuits that can be realised in experiments with neutral atom arrays.

Abstract: We develop a simple compiler that generically adds publicly-verifiable deletion to a variety of cryptosystems. Our compiler only makes use of one-way functions (or one-way state generators, if we allow the public verification key to be quantum). Previously, similar compilers either relied on the use of indistinguishability obfuscation (Bartusek et. al., ePrint:2023/265) or almost-regular one-way functions (Bartusek, Khurana and Poremba, arXiv:2303.08676).