arXiv subjects

Tatsuhiko Shirai

Publications and source records attributed to Tatsuhiko Shirai.

At least 19 recordsLinked to original sources

arXiv2026

Quasi-adiabatic thermal ensemble preparation in the thermodynamic limit

We investigate a quasi-adiabatic thermal process for preparing finite-temperature ensembles in the thermodynamic limit. The process gradually transforms a thermal ensemble of a noninteracting system into that of an interacting system of interest over a finite operation time, with the temperature controlled by parameters associated with the entropy of the initial state. We analyze this process in both nonintegrable and integrable spin chains with translational invariance. For the nonintegrable case, numerical simulations combined with a thermodynamic argument indicate that the thermal properties of local observables are accurately reproduced with a single parameter, although the operation time increases exponentially with precision. In contrast, for the integrable transverse-field Ising model, we analytically show that an extensive number of parameters tied to local conserved quantities is generally necessary, and the performance is affected by the presence of a quantum phase transition. These results clarify the potential and limitations of the quasi-adiabatic thermal process for an ensemble preparation and highlight the role of integrability in determining its efficiency.

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arXiv2025

Compressed space quantum approximate optimization algorithm for constrained combinatorial optimization

Combinatorial optimization is a promising area for achieving quantum speedup. Quantum approximate optimization algorithm (QAOA) is designed to search for low-energy states of the Ising model, which correspond to near-optimal solutions of combinatorial optimization problems (COPs). However, effectively dealing with constraints of COPs remains a significant challenge. Existing methods, such as tailoring mixing operators, are typically limited to specific constraint types, like one-hot constraints. To address these limitations, we introduce a method for engineering a compressed space that represents the feasible solution space with fewer qubits than the original. Our approach includes a scalable technique for determining the unitary transformation between the compressed and original spaces on gate-based quantum computers. We then propose compressed space QAOA, which seeks near-optimal solutions within this reduced space, while utilizing the Ising model formulated in the original Hilbert space. Experimental results on a quantum simulator demonstrate the effectiveness of our method in solving various constrained COPs.

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arXiv2025

Out-of-time-order correlator computation based on discrete truncated Wigner approximation

We propose a method based on the discrete truncated Wigner approximation (DTWA) for computing out-of-time-order correlators. This method is applied to long-range interacting quantum spin systems where the interactions decay as a power law with distance. As a demonstration, we use a squared commutator of local operators and its higher-order extensions that describe quantum information scrambling under Hamilton dynamics. Our results reveal that the DTWA method accurately reproduces the exact dynamics of the average spreading of quantum information (i.e., the squared commutator) across all time regimes in strongly long-range interacting systems. We also identify limitations in the DTWA method when capturing dynamics in weakly long-range interacting systems and the fastest spreading of quantum information. Then we apply the DTWA method to investigate the system-size dependence of the scrambling time in strongly long-range interacting systems. We reveal that the scaling behavior of the scrambling time for large system sizes qualitatively changes depending on the interaction range. This work provides and demonstrates a new technique to study scrambling dynamics in long-range interacting quantum spin systems.

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arXiv2024

Accelerated Decay due to Operator Spreading in Bulk-Dissipated Quantum Systems

Markovian open many-body quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate towards the stationary state, but it has recently been pointed out that the spectral gap does not necessarily determine the overall relaxation time. Our understanding on the relaxation process before the asymptotically long-time regime is still limited. We here present a collective relaxation dynamics of autocorrelation functions in the stationary state. As a key quantity in the analysis, we introduce the instantaneous decay rate, which characterizes the transient relaxation and converges to the conventional asymptotic decay rate in the long-time limit. Our theory predicts that a bulk-dissipated system generically shows an accelerated decay before the asymptotic regime due to the scrambling of quantum information associated with the operator spreading.

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arXiv2024

Toward Practical Benchmarks of Ising Machines: A Case Study on the Quadratic Knapsack Problem

Combinatorial optimization has wide applications from industry to natural science. Ising machines bring an emerging computing paradigm for efficiently solving a combinatorial optimization problem by searching a ground state of a given Ising model. Current cutting-edge Ising machines achieve fast sampling of near-optimal solutions of the max-cut problem. However, for problems with additional constraint conditions, their advantages have been hardly shown due to difficulties in handling the constraints. In this work, we focus on benchmarks of Ising machines on the quadratic knapsack problem (QKP). To bring out their practical performance, we propose fast two-stage post-processing for Ising machines, which makes handling the constraint easier. Simulation based on simulated annealing shows that the proposed method substantially improves the solving performance of Ising machines and the improvement is robust to a choice of encoding of the constraint condition. Through evaluation using an Ising machine called Amplify Annealing Engine, the proposed method is shown to dramatically improve its solving performance on the QKP. These results are a crucial step toward showing advantages of Ising machines on practical problems involving various constraint conditions.

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arXiv2024

Post-processing variationally scheduled quantum algorithm for constrained combinatorial optimization problems

We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a quantum annealer or gate-type quantum device. Variational methods are used to find an optimal schedule function that leads to high-quality solutions in a short amount of time. Post-processing techniques convert the output solutions of the quantum devices to satisfy the constraints of the COPs. pVSQA combines the variational methods and the post-processing technique. We obtain a sufficient condition for constrained COPs to apply pVSQA based on a greedy post-processing algorithm. We apply the proposed method to two constrained NP-hard COPs: the graph partitioning problem and the quadratic knapsack problem. pVSQA on a simulator shows that a small number of variational parameters is sufficient to achieve a (near-)optimal performance within a predetermined operation time. Then building upon the simulator results, we implement pVSQA on a quantum annealer and a gate-type quantum device. The experimental results demonstrate the effectiveness of our proposed method.

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arXiv2022

Symmetrized Liouvillian Gap in Markovian Open Quantum Systems

Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate towards the steady state, but it does not necessarily give a correct estimate of the relaxation time because the crossover time to the asymptotic regime may be too long. We here give a rigorous upper bound on the transient decay of auto-correlation functions in the steady state by introducing the symmetrized Liouvillian gap. The standard Liouvillian gap and the symmetrized one are identical in an equilibrium situation but differ from each other in the absence of the detailed balance condition. It is numerically shown that the symmetrized Liouvillian gap always give a correct upper bound on the decay of the auto-correlation function, but the standard Liouvillian gap does not.

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arXiv2021

Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder

This study investigates the dynamical critical exponent of disordered Ising chains under transverse fields to examine the effect of a correlated disorder on quantum phase transitions. The correlated disorder, where the on-site transverse field depends on the nearest-neighbor coupling strengths connecting the site, gives a qualitatively different result from the uncorrelated disorder. In the uncorrelated disorder cases where the transverse field is either homogeneous over sites or random independently of the nearest-neighbor coupling strengths, the dynamical critical exponent is infinite. In contrast, in the presence of the correlated disorder, we analytically show that the dynamical critical exponent is finite. We also show that the dynamical critical exponent depends on the tuning process of the transverse field strengths.

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arXiv2020

Tensor-network approach to thermalization in open quantum many-body systems

We investigate the relaxation dynamics of open non-integrable quantum many-body systems in the thermodynamic limit by using a tensor-network formalism. We simulate the Lindblad quantum master equation (LQME) of infinite systems by making use of the uniform matrix product operators (MPO) as the ansatz of their density matrices. Furthermore, we establish a method to measure the thermodynamic equivalence between two states described by the uniform MPOs. We numerically show that when an initial state of the LQME is a thermal Gibbs state, a time evolved state is always indistinguishable from a Gibbs state with a time-dependent effective temperature in the weak-dissipation and thermodynamic limit.

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arXiv2020

Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground (lowest-energy) state of the logical Ising model. When connectivity is restricted on Ising machines, ME is required for mapping from the logical Ising model to a physical Ising model, which corresponds to a specific Ising machine. Herein we discuss the guiding principle of ME design to achieve a high performance in Ising machines. We derive the proposed ME based on a theoretical argument of statistical mechanics. The performance of the proposed ME is compared with two existing types of MEs for different benchmarking problems. Simulated annealing shows that the proposed ME outperforms existing MEs for all benchmarking problems, especially when the distribution of the degree in a logical Ising model has a large standard deviation. This study validates the guiding principle of using statistical mechanics for ME to realize fast and high-precision solvers for combinatorial optimization problems.

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arXiv2020

Resolving Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems

The gap of the Liouvillian spectrum gives the asymptotic decay rate of a quantum dissipative system, and therefore its inverse has been identified as the slowest relaxation time. In contrary to this common belief, we show that the relaxation time due to diffusive transports in a boundary dissipated many-body quantum system is determined not by the gap or low-lying eigenvalues of the Liouvillian but by superexponentially large expansion coefficients for Liouvillian eigenvectors with non-small eigenvalues at an initial state. This finding resolves an apparent discrepancy reported in the literature between the inverse of the Liouvillian gap and the relaxation time in dissipative many-body quantum systems.

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arXiv2020

Thermalization in open many-body systems based on eigenstate thermalization hypothesis

We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at an effective temperature gives a good description of the steady state provided that the system Hamiltonian obeys the eigenstate thermalization hypothesis (ETH) and the perturbation theory in the weak system-environment coupling is valid in the thermodynamic limit. We derive a criterion to guarantee the validity of the perturbation theory, which is satisfied in the thermodynamic limit for sufficiently weak dissipation when the Liouvillian is gapped for bulk-dissipated systems, while the perturbation theory breaks down in boundary-dissipated chaotic systems due to the presence of diffusive transports. We numerically confirm these theoretical predictions. This work suggests a connection between steady states of macroscopic open quantum systems and the ETH.

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arXiv2019

Dynamical phase transition in Floquet optical bistable systems: An approach from finite-size quantum systems

We study a dynamical phase transition in optical bistable systems subject to a time-periodic driving field. The phase transition occurs in the structure of limit cycle as a function of the frequency of the driving field. In the thermodynamic limit, a single limit cycle is divided into two separated limit cycles at the transition point. In finite-size systems, however, there is always a single limit cycle due to the quantum tunneling effect. We use a Floquet dissipative map, which is a time-evolution operator over one period in a dynamics given by a quantum master equation, and discuss the decay rate of relaxation dynamics into the limit cycle based on the dominant eigenvalue of the map. We found that the decay rate exhibits qualitatively different system-size dependence before and after the phase transition, and it shows a finite-size scaling of spinodal phenomena around the transition point. The present work provides a systematic way of studying dynamical phase transition observed in time-periodically driven open systems in terms of the Floquet dissipative map.

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arXiv2019

Microscopic Description of Yielding in Glass Based on Persistent Homology

Persistent homology (PH) was applied to probe the structural changes of glasses under shear. PH associates each local atomistic structure in an atomistic configuration to a geometric object, namely, a hole, and evaluates the robustness of these holes against noise. We found that the microscopic structures were qualitatively different before and after yielding. The structures before yielding contained robust holes, the number of which decreased after yielding. We also observed that the structures after yielding approached those of quickly quenched glass. This work demonstrates the crucial role of robust holes in yielding and provides an interpretation based on geometry.

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arXiv2018

Optical Bistability in a Low Photon-Density Regime

We give a microscopic description of the optical bistability, where the transmission coefficient has two different values as a function of input light intensity, and the system exhibits a discontinuous jump with a hysteresis loop. We developed an efficient numerical algorithm to treat the quantum master equation for hybridized systems of many photons and a large number of two-level atoms. By using this method, we characterize the bistability from the viewpoint of eigenmodes and eigenvalues of the time evolution operator of the quantum master equation. We investigate the optical bistability within the low photon-density regime, where the hybridization of photon and atom degrees of freedom occurs and the resonance spectrum has a double peak structure. We compared it with the standard optical bistability between the low photon-density regime and the high photon-density regime, where the photons can be treated as a classical electromagnetic field and the resonance spectrum has a single peak structure. We discuss the steady-state properties of the optical bistability: dependencies of the photon number density on the intensity and the double peak structure of the photon number distribution inside the bistable region. As for the dynamical properties, we find that the relaxation timescale shows an exponential growth with the system size, and reveal how the hysteresis loop of the optical bistability depends on the size of the system and the sweeping rate of the driving amplitude. Finally, by investigating the effects of detuning frequency of the input field, we clarify the characteristic properties of the present optical bistability within the low photon-density regime, which are qualitatively different from the standard optical bistable phenomena.

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arXiv2018

Floquet-Gibbs state in open quantum systems

We study long-time asymptotic states of periodically driven quantum systems coupled to a thermal bath. In order to describe a class of such a system, we introduce the Floquet-Gibbs state, i.e. the state whose density matrix is diagonalized in the basis of the Floquet state of the system Hamiltonian, and its diagonal element obeys the Boltzmann distribution over its Floquet quasienergy. We obtain sufficient conditions for the realization of the Floquet-Gibbs state in a system with infinitesimal system-bath coupling [T. Shirai, et al., Phys. Rev. E 91, 030101 (2015)]. These conditions severely restrict a class of suitable physical models attaining the Floquet-Gibbs state. We also show that some of the conditions can be lifted by imposing conditions on timescales of the thermal bath with the aid of the truncated Floquet Hamiltonian in the Floquet-Magnus expansion [T. Shirai, et al., New Journal of Physics 18, 053008 (2016)]. In this paper we give a overview of this theory and reconsider it by looking at the dynamics from a rotating frame.

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arXiv2016

Effective Floquet-Gibbs states for dissipative quantum systems

A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown that in the limit of an infinitesimal coupling, using so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet-Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet-Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet-Gibbs states.

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arXiv2015

Condition for emergence of the Floquet-Gibbs state in periodically driven open systems

We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the driving field at different times commute, and (iii) the Hamiltonians of the driving field and of the interaction between the relevant system and the thermal bath commute. It is shown that the steady state is described by the Gibbs distribution of the Floquet states of the relevant system at the temperature of the thermal bath.

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