Quantum Physics (quant-ph)

Abstract: We develop a general formulation of quantum statistical mechanics in terms or probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The continuity equation for any closed or open system suggests a natural Bohmian interpretation in terms of microscopic particle trajectories, that make the same measurable predictions as standard quantum theory. The microscopic trajectories are not directly observable, but provide a general, simple and intuitive microscopic interpretation of macroscopic phenomena in quantum statistical mechanics. In particular, we discuss how various notions of entropy, proper and improper mixtures, and thermodynamics are understood from the Bohmian perspective.

Abstract: The expectations arising from the latest achievements in the quantum computing field are causing that researchers coming from classical artificial intelligence to be fascinated by this new paradigm. In turn, quantum computing, on the road towards usability, needs classical procedures. Hybridization is, in these circumstances, an indispensable step but can also be seen as a promising new avenue to get the most from both computational worlds. Nonetheless, hybrid approaches have now and will have in the future many challenges to face, which, if ignored, will threaten the viability or attractiveness of quantum computing for real-world applications. To identify them and pose pertinent questions, a proper characterization of the hybrid quantum computing field, and especially hybrid solvers, is compulsory. With this motivation in mind, the main purpose of this work is to propose a preliminary taxonomy for classifying hybrid schemes, and bring to the fore some questions to stir up researchers minds about the real challenges regarding the application of quantum computing.

Abstract: We consider a quantum Otto cycle with a $q$-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter $q$ on the work and efficiency of the cycle. In usual quantum Otto cycle, a Hamiltonian parameter is varied during the quantum adiabatic stages while the quantum statistical character of the working substance remains fixed. We point out that even if the Hamiltonian parameters are not changing, work can be harvested by quantum statistical changes of the working substance. Work extraction from thermal resources using quantum statistical mutations of the working substance makes a quantum Otto cycle without any classical analog.

Abstract: Tensor networks have historically proven to be of great utility in providing compressed representations of wave functions that can be used for calculation of eigenstates. Recently, it has been shown that a variety of these networks can be leveraged to make real time non-equilibrium simulations of dynamics involving the Feynman-Vernon influence functional more efficient. In this work, tensor networks are utilized for calculating equilibrium correlation function for open quantum systems using the path integral methodology. These correlation functions are of fundamental importance in calculations of rates of reactions, simulations of response functions and susceptibilities, spectra of systems, etc. The influence of the solvent on the quantum system is incorporated through an influence functional, whose unconventional structure motivates the design of a new optimal matrix product-like operator that can be applied to the so-called path amplitude matrix product state. This complex time tensor network path integral approach provides an exceptionally efficient representation of the path integral enabling simulations for larger systems strongly interacting with baths and at lower temperatures out to longer time. The design and implementation of this method is discussed along with illustrations from rate theory, symmetrized spin correlation functions, dynamical susceptibility calculations and quantum thermodynamics.

Abstract: Bell diagonal states constitute a well-studied family of bipartite quantum states that arise naturally in various contexts in quantum information. In this paper we generalize the notion of Bell diagonal states to the case of unequal local dimensions and investigate their entanglement properties. We extend the family of entanglement criteria of Sarbicki et al. to non-Hermitian operator bases to construct entanglement witnesses for the class of generalized Bell diagonal states. We then show how to optimize the witnesses with respect to noise robustness. Finally, we use these witnesses to construct bound entangled states that are not detected by the usual computable cross norm or realignment and de Vicente criteria.

Abstract: In this work we introduce a new framework - Dirac's Hamiltonian formalism of constraint systems - to study different types of Superconducting Quantum Circuits (SQC) in a {\it{unified}} and unambiguous way. The Lagrangian of a SQC reveals the constraints, that are classified in a Hamiltonian framework, such that redundant variables can be removed to isolate the canonical degrees of freedom for subsequent quantization of the Dirac Brackets via a generalized Correspondence Principle. This purely algebraic approach makes the application of concepts such as graph theory, null vector, loop charge,\ etc that are in vogue, (each for a specific type of circuit), completely redundant.

Abstract: We simulate coherent driven free dissipative Kerr nonlinear system numerically using time evolving block decimation (TEBD) algorithm and time propagation on the Heisenberg equation of motion using Eulers method to study how the numerical results are analogous to classical bistability. The system evolves through different trajectories to stabilize different branches for different external drives and initial conditions. The Wigner state reprentation confirms the system to suffer a residual effect of initial state throughout the non-classical dynamical evolution and the steady state of the system. Furthermore, we also see the numerically simulated spectral density remains significantly different from analytical counterparts when initial states do not lie to the same branch of the final state.

Abstract: Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in near-term quantum devices. While the VQE is traditionally tailored to determine the ground state wavefunction with the underlying Rayleigh-Ritz principle, the access to specific symmetry-adapted excited states remains elusive. This often requires high depth circuit or additional ancilla qubits along with prior knowledge of the ground state wavefunction. We propose a unified VQE framework that treats the ground and excited states in the same footings. With the knowledge of the irreducible representations of the spinorbitals, we construct a multi-determinantal reference that is adapted to a given spatial symmetry where additionally, the determinants are entangled through appropriate Clebsch-Gordan coefficients to ensure the desired spin-multiplicity. We introduce the notion of totally symmetric, spin-scalar unitary which maintains the purity of the reference at each step of the optimization. The state-selectivity safeguards the method against any variational collapse while leading to any targeted low-lying eigenroot of arbitrary symmetry. The direct access to the excited states shields our approach from the cumulative error that plagues excited state calculations in a quantum computer and with few parameter count, it is expected to be realized in near-term quantum devices.

Abstract: The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and refining it using QA. In previous studies, such variables were determined using molecular dynamics (MD) as a continuous optimization method. We propose a method that uses the simple continuous relaxation technique called linear programming (LP) relaxation. Our method demonstrated superiority through comparative experiments with the minimum vertex cover problem versus the previous MD-based approach. Furthermore, the hybrid approach of LP relaxation and simulated annealing showed advantages in accuracy and speed compared to solving with simulated annealing alone.

Abstract: According to Bell's theorem, certain entangled states cannot be simulated classically using local hidden variables (LHV). But if can we augment LHV by classical communication, how many bits are needed to simulate them? There is a strong evidence that a single bit of communication is powerful enough to simulate projective measurements on any two-qubit entangled state. In this study, we present Bell-like scenarios where bipartite correlations resulting from projective measurements on higher dimensional states cannot be simulated with a single bit of communication. These include a three-input, a four-input, a seven-input, and a 63-input bipartite Bell-like inequality with 80089, 64, 16, and 2 outputs, respectively. Two copies of emblematic Bell expressions, such as the Magic square pseudo-telepathy game, prove to be particularly powerful, requiring a $16\times 16$ state to beat the one-bit classical bound, and look a promising candidate for implementation on an optical platform.

Abstract: A large class of problems in the current era of quantum devices involve interfacing between the quantum and classical system. These include calibration procedures, characterization routines, and variational algorithms. The control in these routines iteratively switches between the classical and the quantum computer. This results in the repeated compilation of the program that runs on the quantum system, scaling directly with the number of circuits and iterations. The repeated compilation results in a significant overhead throughout the routine. In practice, the total runtime of the program (classical compilation plus quantum execution) has an additional cost proportional to the circuit count. At practical scales, this can dominate the round-trip CPU-QPU time, between 5% and 80%, depending on the proportion of quantum execution time. To avoid repeated device-level compilation, we identify that machine code can be parametrized corresponding to pulse/gate parameters which can be dynamically adjusted during execution. Therefore, we develop a device-level partial-compilation (DLPC) technique that reduces compilation overhead to nearly constant, by using cheap remote procedure calls (RPC) from the QPU control software to the CPU. We then demonstrate the performance speedup of this on optimal pulse calibration, system characterization using randomized benchmarking (RB), and variational algorithms. We execute this modified pipeline on real trapped-ion quantum computers and observe significant reductions in compilation time, as much as 2.7x speedup for small-scale VQE problems.

Abstract: It is essential to select efficient topology of parameterized quantum circuits (PQCs) in variational quantum algorithms (VQAs). However, there are problems in current circuits, i.e. optimization difficulties caused by too many parameters or performance is hard to guarantee. How to reduce the number of parameters (number of single-qubit rotation gates and 2-qubit gates) in PQCs without reducing the performance has become a new challenge. To solve this problem, we propose a novel topology, called Block-Ring (BR) topology, to construct the PQCs. This topology allocate all qubits to several blocks, all-to-all mode is adopt inside each block and ring mode is applied to connect different blocks. Compared with the pure all-to-all topology circuits which own the best power, BR topology have similar performance and the number of parameters and 2-qubit gate reduced from 0(n^2) to 0(mn) , m is a hyperparameter set by ourselves. Besides, we compared BR topology with other topology circuits in terms of expressibility and entangling capability. Considering the effects of different 2-qubit gates on circuits, we also make a distinction between controlled X-rotation gates and controlled Z-rotation gates. Finally, the 1- and 2-layer configurations of PQCs are taken into consideration as well, which shows the BR's performance improvement in the condition of multilayer circuits.

Abstract: Many quantum algorithms rely on the measurement of complex quantum amplitudes. Standard approaches to obtain the phase information, such as the Hadamard test, give rise to large overheads due to the need for global controlled-unitary operations. We introduce a quantum algorithm based on complex analysis that overcomes this problem for amplitudes that are a continuous function of time. Our method only requires the implementation of real-time evolution and a shallow circuit that approximates a short imaginary-time evolution. We show that the method outperforms the Hadamard test in terms of circuit depth and that it is suitable for current noisy quantum computers when combined with a simple error-mitigation strategy.

Abstract: We address the problem of evaluating the difference between quantum states before and after being affected by errors encoded in unitary transformations. Standard distance functions, e.g., the Bures length, are not fully adequate for such a task. Weighted distances are instead appropriate information measures to quantify distinguishability of multipartite states. Here, we employ the previously introduced weighted Bures length and the newly defined weighted Hilbert-Schmidt distance to quantify how much single-qubit Pauli errors alter cluster states. We find that different errors of the same dimension change cluster states in a different way, i.e., their detectability is in general different. Indeed, they transform an ideal cluster state into a state whose weighted distance from the input depends on the specific chosen Pauli rotation, as well as the position of the affected qubit in the graph related to the state. As these features are undetected by using standard distances, the study proves the usefulness of weighted distances to monitor key but elusive properties of many-body quantum systems.

Abstract: A limited set of tools exist for assessing whether the behavior of quantum machine learning models diverges from conventional models, outside of abstract or theoretical settings. We present a systematic application of explainable artificial intelligence techniques to analyze synthetic data generated from a hybrid quantum-classical neural network adapted from twenty different real-world data sets, including solar flares, cardiac arrhythmia, and speech data. Each of these data sets exhibits varying degrees of complexity and class imbalance. We benchmark the quantum-generated data relative to state-of-the-art methods for mitigating class imbalance for associated classification tasks. We leverage this approach to elucidate the qualities of a problem that make it more or less likely to be amenable to a hybrid quantum-classical generative model.

Abstract: We report an experimental demonstration of anti-parity-time (anti-PT) symmetric optical four-wave mixing in thermal Rubidium vapor, where the propagation of two conjugate optical fields in a double-$\Lambda$ scheme is governed by a non-Hermitian Hamiltonian. We are particularly interested in studying quantum intensity correlations between the two conjugate fields near the exceptional point, taking into account loss and accompanied Langevin noise. Our experimental measurements of classical four-wave mixing gain and the associated two-mode relative-intensity squeezing are in reasonable agreement with the theoretical predictions.