Quantum Physics (quant-ph)

Abstract: The variational quantum eigensolver (VQE) stands as a prominent quantum-classical hybrid algorithm for near-term quantum computers to obtain the ground states of molecular Hamiltonians in quantum chemistry. However, due to the non-commutativity of the Pauli operators in the Hamiltonian, the number of measurements required on quantum computers increases significantly as the system size grows, which may hinder practical applications of VQE. In this work, we present a protocol termed joint Bell measurement VQE (JBM-VQE) to reduce the number of measurements and speed up the VQE algorithm. Our method employs joint Bell measurements, enabling the simultaneous measurement of the absolute values of all expectation values of Pauli operators present in the Hamiltonian. In the course of the optimization, JBM-VQE estimates the absolute values of the expectation values of the Pauli operators for each iteration by the joint Bell measurement, while the signs of them are measured less frequently by the conventional method to measure the expectation values. Our approach is based on the empirical observation that the signs do not often change during optimization. We illustrate the speed-up of JBM-VQE compared to conventional VQE by numerical simulations for finding the ground states of molecular Hamiltonians of small molecules, and the speed-up of JBM-VQE at the early stage of the optimization becomes increasingly pronounced in larger systems. Our approach based on the joint Bell measurement is not limited to VQE and can be utilized in various quantum algorithms whose cost functions are expectation values of many Pauli operators.

Abstract: It is rigorously shown that an appropriate quantum annealing for any finite-dimensional spin system has no quantum first-order transition in transverse magnetization. This result can be applied to finite-dimensional spin-glass systems, where the ground state search problem is known to be hard to solve. Consequently, it is strongly suggested that the quantum first-order transition in transverse magnetization is not fatal to the difficulty of combinatorial optimization problems in quantum annealing.

Abstract: We investigate the group structure of center-preserving automorphisms of the finite Heisenberg group over $\mathbb Z_N$ with $U(1)$ extension, which arises in finite-dimensional quantum mechanics on a discrete phase space. Constructing an explicit splitting, it is shown that, for $N=2(2k+1)$, the group is isomorphic to the semidirect product of $Sp_N$ and $\mathbb Z_N^2$. Moreover, when N is divisible by $2l (l \ge 2)$, the group has a non-trivial 2-cocycle, and its explicit form is provided. By utilizing the splitting, it is demonstrated that the corresponding projective Weil representation can be lifted to linear representation.

Abstract: Multipartite generalizations of spin coherent states are introduced and analyzed. These are the spin analogues of multimode optical coherent states as used in continuous variable quantum information, but generalized to possess full spin symmetry. Two possible generalizations are given, one which is a simple tensor product of a given multipartite quantum state. The second generalization uses the bosonic formulation in the Jordan-Schwinger map, which we call spinor states. In the unipartite case, spinor states are equivalent to spin coherent states, however in the multipartite case, they are no longer equivalent. Some fundamental properties of these states are discussed, such as their observables and covariances with respect to symmetric operators, form preserving transformations, and entanglement. We discuss the utility of such multipartite spin coherent and spinor states as a way of storing quantum information.

Abstract: We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need to be used, the order of measurements is critical for quickly assessing accuracy. We propose and compare different strategies to compute optimal or suboptimal measurement sequences either relying solely on a priori information, i.e., the target state for state preparation, or actively adapting the sequence to the previously obtained measurements. Numerical simulations show that the proposed algorithms reduce significantly the number of measurements needed for verification, and indicate an advantage for the adaptive protocol especially assessing faulty preparations.

Abstract: The past decade has seen considerable progress in quantum hardware in terms of the speed, number of qubits and quantum volume which is defined as the maximum size of a quantum circuit that can be effectively implemented on a near-term quantum device. Consequently, there has also been a rise in the number of works based on the applications of Quantum Machine Learning (QML) on real hardware to attain quantum advantage over their classical counterparts. In this survey, our primary focus is on selected supervised and unsupervised learning applications implemented on quantum hardware, specifically targeting real-world scenarios. Our survey explores and highlights the current limitations of QML implementations on quantum hardware. We delve into various techniques to overcome these limitations, such as encoding techniques, ansatz structure, error mitigation, and gradient methods. Additionally, we assess the performance of these QML implementations in comparison to their classical counterparts. Finally, we conclude our survey with a discussion on the existing bottlenecks associated with applying QML on real quantum devices and propose potential solutions for overcoming these challenges in the future.

Abstract: In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of particle. In laboratory frame, a generalized Lippmann-Schwinger scattering equation is derived. We emphasized that the derivation is rigorous, even for treating infinitesimals. No manual operation such as analytical continuation is allowed. In the case that before scattering N particles are plane waves and after the scattering they are new plane waves, the transition amplitude and transition probability are given and the generalized S matrix is presented. It is proved that the transition probability from a set of plane waves to a new set of plane waves of the N particles equal to that of the reciprocal process. The generalized theory is applied to the cases of one- and two-particle scattering as two examples. When applied to single-particle scattering problems, our generalized formalism degrades to that usually seen in the literature. When our generalized theory is applied to two-particle scattering problems, the formula of the transition probability of two-particle collision is given. It is shown that the transition probability of the scattering of two free particles is identical to that of the reciprocal process. This transition probability and the identity are needed in deriving Boltzmann transport equation in statistical mechanics. The case of identical particles is also discussed.

Abstract: Digital-analog quantum computing is a computational paradigm which employs an analog Hamiltonian resource together with single-qubit gates to reach universality. The original protocol to simulate an arbitrary Hamiltonian was explicitly constructed for an Ising Hamiltonian as the analog resource. Here, we extend this scheme to employ an arbitrary two-body source Hamiltonian, enhancing the experimental applicability of this computational paradigm. We show that the simulation of an arbitrary two-body target Hamiltonian of $n$ qubits requires at most $\mathcal{O}(n^2)$ analog blocks. Additionally, for further reducing the number of blocks, we propose an approximation technique by fixing the number of digital-analog blocks in which we optimize the angles of the single-qubit rotations and the times of the analog blocks. These techniques provide a new useful toolbox for enhancing the applicability and impact of the digital-analog paradigm on NISQ devices.

Abstract: The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can be seen as measures of entanglement. We study the case of real 3-qutrit systems and discover a new set of maximally entangled states (from the point of view of maximizing the hyperdeterminant). We also study the basic fundamental invariants and find real 3-qutrit states that maximize their absolute values. It is notable that the Aharonov state is a simultaneous maximizer for all 3 fundamental invariants. We also study the evaluation of these invariants on random real 3-qutrit systems and analyze their behavior using histograms and level-set plots. Finally, we show how to evaluate these invariants on any 3-qutrit state using basic matrix operations.

Abstract: In quantum illumination (QI) the non-classical correlations between continuous variable (CV) entangled modes of radiation are exploited to detect the presence of a target embedded in thermal noise. The extreme environment where QI outperforms its optimal classical counterpart suggests that applications in the microwave domain would benefit the most from this new sensing paradigm. However all the proposed QI receivers rely on ideal photon counters or detectors, which are not currently feasible in the microwave domain. Here we propose a new QI receiver that utilizes a CV controlled not gate (CNOT) in order to perform a joint measurement on a target return and its retained twin. Unlike other QI receivers, the entire detection process is carried out by homodyne measurements and square-law detectors. The receiver exploits two squeezed ancillary modes as a part of the gate's operation. These extra resources are prepared offline and their overall gain is controlled passively by a single beamsplitter parameter. We compare our model to other QI receivers and demonstrate its operation regime where it outperforms others and achieves optimal performance. Although the main focus of this study is microwave quantum sensing applications, our proposed device can be built as well in the optical domain, thus rendering it as a new addition to the quantum sensing toolbox in a wider sense.

Abstract: This paper focuses on the construction of a general parametric model that can be implemented executing multiple swap tests over few qubits and applying a suitable measurement protocol. The model turns out to be equivalent to a two-layer feedforward neural network which can be realized combining small quantum modules. The advantages and the perspectives of the proposed quantum method are discussed.

Abstract: Understanding the ultimate rate at which information propagates is a pivotal issue in nonequilibrium physics. Nevertheless, the task of elucidating the propagation speed inherent in quantum bosonic systems presents challenges due to the unbounded nature of their interactions. In this Letter, we tackle the problem of particle transport in long-range bosonic systems through the lens of both quantum speed limits and the Lieb-Robinson bound. Employing a unified approach based on optimal transport theory, we rigorously prove that the minimum time required for macroscopic particle transport is always bounded by the distance between the source and target regions, while retaining its significance even in the thermodynamic limit. Furthermore, we derive an upper bound for the probability of observing a specific number of bosons inside the target region, thereby providing additional insights into the dynamics of particle transport. Our results hold true for arbitrary initial states under both long-range hopping and long-range interactions, thus resolving an open problem of particle transport in generic bosonic systems.

Abstract: The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently from the position and momentum expectation values. They are extra degrees of quantum mechanics compared to classical mechanics, and encode the shape of wave-packets. Following the logic that quantum mechanics must be lifted to quantum field theory, we discuss the quantization of the quantum uncertainty as an operator acting on wave-functions over field space and derive its discrete spectrum, inherited from the $\textrm{sl}_{2}$ Lie algebra formed by the operators $\hat{x}^{2}$, $\hat{p}^{2}$ and $\widehat{xp}$. We further show how this spectrum appears in the value of the coupling of the effective conformal potential driving the evolution of extended Gaussian wave-packets according to Schr\"odinger equation, with the quantum uncertainty playing the same role as an effective intrinsic angular momentum. We conclude with an open question: is it possible to see experimental signatures of the quantization of the quantum uncertainty in non-relativistic physics, which would signal the departure from quantum mechanics to a QFT regime?

Abstract: Quantum information protocols are often designed in the ideal situation with no decoherence. However, in real setup, these protocols are subject to the decoherence and thus reducing fidelity of the measurement outcome. In this work, we analyze the effect of state dependent bath on the quantum correlations and the fidelity of a single qubit teleportation. We model our system-bath interaction as qubits interacting with a common bath of bosons, and the state dependence of the bath is generated through a projective measurement on the joint state in thermal equilibrium. The analytic expressions for the time evolution of entanglement, Negativity and average fidelity of quantum teleportation are calculated. It is shown that due to the presence of initial system-bath correlations, the system maintains quantum correlations for long times. Furthermore, due to the presence of finite long time entanglement of the quantum channel, the average fidelity is shown to be higher than its classical value.

Abstract: To date, dissipative phase transitions (DPTs) have mostly been studied for quantum systems coupled to idealized Markovian (memoryless) environments, where the closing of the Liouvillian gap constitutes a hallmark. Here, we extend the spectral theory of DPTs to arbitrary non-Markovian systems and present a general and systematic method to extract their signatures, which is fundamental for the understanding of realistic materials and experiments such as in the solid-state, cold atoms, cavity or circuit QED. We first illustrate our theory to show how memory effects can be used as a resource to control phase boundaries in a model exhibiting a first-order DPT, and then demonstrate the power of the method by capturing all features of a challenging second-order DPT in a two-mode Dicke model for which previous attempts had fail up to now.

Abstract: We demonstrate a novel experimental technique for quantum-state tomography of the collective density matrix. It is based on measurements of the polarization of light, traversing the atomic vapor. To assess the technique's robustness against errors, experimental investigations are supported with numerical simulations. This not only allows to determine the fidelity of the reconstruction, but also to analyze the quality of the reconstruction for specific experimental parameters light tuning and number of measurements). By utilizing the so-called conditional number, we demonstrate that the reconstruction can be optimized for a specific tuning of the system parameters, and further improvement is possible by selective repetition of the measurements. Our results underscore the potential high-fidelity quantum-state reconstruction while optimizing measurement resources.

Abstract: To leverage the full potential of quantum error-correcting stabilizer codes it is crucial to have an efficient and accurate decoder. Accurate, maximum likelihood, decoders are computationally very expensive whereas decoders based on more efficient algorithms give sub-optimal performance. In addition, the accuracy will depend on the quality of models and estimates of error rates for idling qubits, gates, measurements, and resets, and will typically assume symmetric error channels. In this work, instead, we explore a model-free, data-driven, approach to decoding, using a graph neural network (GNN). The decoding problem is formulated as a graph classification task in which a set of stabilizer measurements is mapped to an annotated detector graph for which the neural network predicts the most likely logical error class. We show that the GNN-based decoder can outperform a matching decoder for circuit level noise on the surface code given only simulated experimental data, even if the matching decoder is given full information of the underlying error model. Although training is computationally demanding, inference is fast and scales approximately linearly with the space-time volume of the code. We also find that we can use large, but more limited, datasets of real experimental data [Google Quantum AI, Nature {\bf 614}, 676 (2023)] for the repetition code, giving decoding accuracies that are on par with minimum weight perfect matching. The results show that a purely data-driven approach to decoding may be a viable future option for practical quantum error correction, which is competitive in terms of speed, accuracy, and versatility.

Abstract: Nitrogen Vacancy Center Ensembles are excellent candidates for quantum sensors due to their vector magnetometry capabilities, deployability at room temperature and simple optical initialization and readout. This work describes the engineering and characterization methods required to control all four Principle Axis Systems (P.A.S.) of NV ensembles in a single crystal diamond without an applied static magnetic field. Circularly polarized microwaves enable arbitrary simultaneous control with spin-locking experiments and collective control using Optimal Control Theory (OCT) in a (100) diamond. These techniques may be further improved and integrated to realize high sensitivity NV-based quantum sensing devices using all four P.A.S. systems.

Abstract: Entropy measures quantify the amount of information and correlations present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and R\'enyi entropies, as well as the measured relative entropy and measured R\'enyi relative entropy. Our approach first parameterizes a variational formula for the measure of interest by a quantum circuit and a classical neural network, and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it as a promising approach for usage in downstream tasks.

Abstract: Randomised measurements provide a way of determining physical quantities without the need for a shared reference frame nor calibration of measurement devices. Therefore, they naturally emerge in situations such as benchmarking of quantum properties in the context of quantum communication and computation where it is difficult to keep local reference frames aligned. In this review, we present the advancements made in utilising such measurements in various quantum information problems focusing on quantum entanglement and Bell inequalities. We describe how to detect and characterise various forms of entanglement, including genuine multipartite entanglement and bound entanglement. Bell inequalities are discussed to be typically violated even with randomised measurements, especially for a growing number of particles and settings. Additionally, we provide an overview of estimating other relevant nonlinear functions of a quantum state or performing shadow tomography from randomised measurements. Throughout the review, we complement the description of theoretical ideas by explaining key experiments.

Abstract: Amid the growing interest in non-Hermitian quantum systems, non-interacting models have received the most attention. Here, through the stochastic series expansion quantum Monte Carlo method, we investigate non-Hermitian physics in interacting quantum systems, e.g., various non-Hermitian quantum spin chains. While calculations yield consistent numerical results under open boundary conditions, non-Hermitian quantum systems under periodic boundary conditions observe an unusual concentration of imaginary-time worldlines over nontrivial winding and require enhanced ergodicity between winding-number sectors for proper convergences. Such nontrivial worldline winding is an emergent physical phenomenon that also exists in other non-Hermitian models and analytical approaches. Alongside the non-Hermitian skin effect and the point-gap spectroscopy, it largely extends the identification and analysis of non-Hermitian topological phenomena to quantum systems with interactions, finite temperatures, biorthogonal basis, and periodic boundary conditions in a novel and controlled fashion. Finally, we study the direct physical implications of such nontrivial worldline winding, which bring additional, potentially quasi-long-range contributions to the entanglement entropy.

Abstract: Random number generators play an essential role in cryptography and key distribution. It is thus important to verify whether the random numbers generated from these devices are genuine and unpredictable by any adversary. Recently, quantum nonlocality has been identified as a resource that can be utilised to certify randomness. Although these schemes are device-independent and thus highly secure, the observation of quantum nonlocality is extremely difficult from a practical perspective. In this work, we provide a scheme to certify unbounded randomness in a semi-device-independent way based on the maximal violation of Leggett-Garg inequalities. Interestingly, the scheme is independent of the choice of the quantum state, and consequently even "quantum" noise could be utilized to self-test quantum measurements and generate unbounded randomness making the scheme highly efficient for practical purposes.

Abstract: The achievement of sufficiently fast interactions between two optical fields at the few-photon level would provide a key enabler for a broad range of quantum technologies. One critical hurdle in this endeavor is the lack of a comprehensive quantum theory of the generation of nonlinearities by ensembles of emitters. Distinct approaches applicable to different regimes have yielded important insights: i) a semiclassical approach reveals that, for many-photon coherent fields, the contributions of independent emitters add independently allowing ensembles to produce strong optical nonlinearities via EIT; ii) a quantum analysis has shown that in the few-photon regime collective coupling effects prevent ensembles from inducing these strong nonlinearities. Rather surprisingly, experimental results with around twenty photons are in line with the semi-classical predictions. Theoretical analysis has been fragmented due to the difficulty of treating nonlinear many-body quantum systems. Here we are able to solve this problem by constructing a powerful theory of the generation of optical nonlinearities by single emitters and ensembles. The key to this construction is the application of perturbation theory to perturbations generated by subsystems. This theory reveals critical properties of ensembles that have long been obscure. The most remarkable of these is the discovery that quantum effects prevent ensembles generating single-photon nonlinearities only within the rotating-wave regime; outside this regime single-photon nonlinearities scale as the number of emitters. The theory we present here also provides an efficient way to calculate nonlinearities for arbitrary multi-level driving schemes, and we expect that it will prove a powerful foundation for further advances in this area.

Abstract: Entangled states shared among distant nodes are frequently used in quantum network applications. When quantum resources are abundant, entangled states can be continuously distributed across the network, allowing nodes to consume them whenever necessary. This continuous distribution of entanglement enables quantum network applications to operate continuously while being regularly supplied with entangled states. Here, we focus on the steady-state performance analysis of protocols for continuous distribution of entanglement. We propose the virtual neighborhood size and the virtual node degree as performance metrics. We utilize the concept of Pareto optimality to formulate a multi-objective optimization problem to maximize the performance. As an example, we solve the problem for a quantum network with a tree topology. One of the main conclusions from our analysis is that the entanglement consumption rate has a greater impact on the protocol performance than the fidelity requirements. The metrics that we establish in this manuscript can be utilized to assess the feasibility of entanglement distribution protocols for large-scale quantum networks.