Updated on 2024/03/29

写真a

 
SHIRAI, Tatsuhiko
 
Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Assistant Professor(without tenure)

Research Experience

  • 2020.04
    -
    Now

    早稲田大学基幹理工学部情報通信学科   講師(任期付)

  • 2019.04
    -
    2020.03

    早稲田大学グリーン・コンピューティング・システム研究機構   次席研究員

  • 2017.01
    -
    2019.03

    東京大学物性研究所   特任研究員

  • 2016.04
    -
    2016.12

    東北大学原子分子材料科学高等研究機構   産学官連携研究員

Education Background

  • 2013.04
    -
    2016.03

    東京大学大学院 理学系研究科 物理学専攻 博士課程  

  • 2011.04
    -
    2013.03

    東京大学大学院 理学系研究科 物理学専攻 修士課程  

  • 2007.04
    -
    2011.03

    The University of Tokyo  

Committee Memberships

  • 2022.04
    -
    Now

    電子情報通信学会  VLSI設計技術研究会専門委員

Professional Memberships

  •  
     
     

    IEEE

  •  
     
     

    日本物理学会

Research Areas

  • Computer system / Mathematical physics and fundamental theory of condensed matter physics

Research Interests

  • 量子アルゴリズム

  • 量子開放系

  • 非平衡統計力学

Awards

  • 2022年度SLDM研究会優秀論文賞

    2022.06   情報処理学会  

  • 第16回若手奨励賞(領域11)

    2022.03   日本物理学会  

  • 第197回SLDM研究会優秀発表賞

    2022.01   情報処理学会  

 

Papers

  • Post-Processing Variationally Scheduled Quantum Algorithm for Constrained Combinatorial Optimization Problems

    Tatsuhiko Shirai, Nozomu Togawa

    IEEE Transactions on Quantum Engineering    2024

    DOI

    Scopus

  • A GPU-based Ising Machine with a Multi-spin-flip Capability for Constrained Combinatorial Optimization

    Satoru Jimbo, Tatsuhiko Shirai, Nozomu Togawa, Masato Motomura, Kazushi Kawamura

    IEEE Access    2024

    DOI

  • Symmetrized Liouvillian Gap in Markovian Open Quantum Systems

    Takashi Mori, Tatsuhiko Shirai

    PHYSICAL REVIEW LETTERS   130 ( 23 )  2023.06

     View Summary

    Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate toward 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 autocorrelation 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 gives a correct upper bound on the decay of the autocorrelation function, but the standard Liouvillian gap does not.

    DOI

    Scopus

    8
    Citation
    (Scopus)
  • Multi-Spin-Flip Engineering in an Ising Machine.

    Tatsuhiko Shirai, Nozomu Togawa

    IEEE Trans. Computers   72 ( 3 ) 759 - 771  2023.03

    Authorship:Lead author, Corresponding author

    DOI

    Scopus

    2
    Citation
    (Scopus)
  • Spin-Variable Reduction Method for Handling Linear Equality Constraints in Ising Machines

    Tatsuhiko Shirai, Nozomu Togawa

    IEEE Transactions on Computers    2023  [Refereed]

    DOI

    Scopus

  • QUBO Matrix Distorting Method for Consumer Applications.

    Tomokazu Yoshimura, Tatsuhiko Shirai, Masashi Tawada, Nozomu Togawa

    ICCE     1 - 6  2022

    DOI

    Scopus

    3
    Citation
    (Scopus)
  • Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder

    Tatsuhiko Shirai, Shu Tanaka

    Annals of Physics     168483 - 168483  2021.12  [Refereed]

    Authorship:Lead author, Corresponding author

    DOI

    Scopus

    3
    Citation
    (Scopus)
  • Tensor network approach to thermalization in open quantum many-body systems

    Hayate Nakano, Tatsuhiko Shirai, Takashi Mori

    Physical Review E   103 ( 4 )  2021.04  [Refereed]

    DOI

    Scopus

    1
    Citation
    (Scopus)
  • Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

    Kensuke Tamura, Tatsuhiko Shirai, Hosho Katsura, Shu Tanaka, Nozomu Togawa

    IEEE Access   9   1 - 1  2021  [Refereed]

    DOI

    Scopus

    23
    Citation
    (Scopus)
  • Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

    Tatsuhiko Shirai, Shu Tanaka, Nozomu Togawa

    IEEE ACCESS   8   210490 - 210502  2020.12  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    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.

    DOI

    Scopus

    8
    Citation
    (Scopus)
  • Resolving Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems

    Takashi Mori, Tatsuhiko Shirai

    PHYSICAL REVIEW LETTERS   125 ( 23 )  2020.06  [Refereed]

     View Summary

    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.

    DOI

    Scopus

    35
    Citation
    (Scopus)
  • Dynamical phase transition in Floquet optical bistable systems: An approach from finite-size quantum systems

    Tatsuhiko Shirai, Synge Todo, Seiji Miyashita

    PHYSICAL REVIEW A   101 ( 1 )  2019.10  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    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.

    DOI

    Scopus

    2
    Citation
    (Scopus)
  • Microscopic Description of Yielding in Glass Based on Persistent Homology

    Tatsuhiko Shirai, Takenobu Nakamura

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   88 ( 7 )  2019.07  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    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.

    DOI

    Scopus

    7
    Citation
    (Scopus)
  • Thermalization in open many-body systems based on eigenstate thermalization hypothesis

    Tatsuhiko Shirai, Takashi Mori

    PHYSICAL REVIEW E   101 ( 4 )  2018.12  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    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.

    DOI

    Scopus

    19
    Citation
    (Scopus)
  • Optical bistability in a low-photon-density regime

    Tatsuhiko Shirai, Synge Todo, Hans de Raedt, Seiji Miyashita

    Physical Review A   98 ( 4 )  2018.10  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    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.

    DOI

  • Floquet–Gibbs state in open quantum systems

    Tatsuhiko Shirai

    The European Physical Journal Special Topics   227 ( 3-4 ) 323 - 333  2018.09  [Refereed]

    Authorship:Lead author, Corresponding author

    DOI

    Scopus

    6
    Citation
    (Scopus)
  • Effective Floquet-Gibbs states for dissipative quantum systems

    Tatsuhiko Shirai, Juzar Thingna, Takashi Mori, Sergey Denisov, Peter Hänggi, Seiji Miyashita

    NEW JOURNAL OF PHYSICS   18 ( 5 )  2015.11  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    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.

    DOI

    Scopus

    52
    Citation
    (Scopus)
  • Condition for emergence of the Floquet-Gibbs state in periodically driven open systems

    Tatsuhiko Shirai

    Physical Review E   91 ( 3 )  2015.03  [Refereed]

    Authorship:Lead author, Corresponding author

    DOI

  • Photon and spin dependence of the resonance line shape in the strong coupling regime

    Seiji Miyashita, Tatsuhiko Shirai, Takashi Mori, Hans De Raedt, Sylvain Bertaina, Irinel Chiorescu

    JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS   45 ( 12 )  2012.06  [Refereed]

     View Summary

    We study the quantum dynamics of a spin ensemble coupled to cavity photons. Recently, related experimental results have been reported, showing the existence of the strong coupling regime in such systems. We study the eigenenergy distribution of the multi-spin system (following the Tavis-Cummings model) which shows a peculiar structure as a function of the number of cavity photons and of spins. We study how this structure causes changes in the spectrum of the admittance in the linear response theory, and also in the frequency dependence of the excited quantities in the stationary state under a probing field. In particular, we investigate how the structure of the higher excited energy levels changes the spectrum from a double-peak structure (the so-called vacuum-field Rabi splitting) to a single-peak structure. We also point out that the spin dynamics in the region of the double-peak structure corresponds to recent experiments using cavity ringing, while in the region of the single-peak structure, it corresponds to the coherent Rabi oscillation in a driving electromagnetic field. Using a standard Lindblad-type mechanism, we study the effect of dissipation on the line width and separation in the computed spectra. In particular, we study the relaxation of the total spin in the general case of a spin ensemble in which the total spin of the system is not specified. The theoretical results are correlated with experimental evidence of the strong coupling regime, achieved with a spin-1/2 ensemble.

    DOI

    Scopus

    7
    Citation
    (Scopus)
  • Novel symmetry-broken phase in a driven cavity system in the thermodynamic limit

    Tatsuhiko Shirai, Takashi Mori, Seiji Miyashita

    Journal of Physics B: Atomic, Molecular and Optical Physics   47 ( 2 )  2012.04  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    We study non-equilibrium stationary states of a cavity system consisting of
    many atoms interacting with a quantized cavity field mode, under a driving
    field in a dissipative environment. We derive a quantum master equation which
    is suitable for treating systems with a strong driving field and a strong
    atom-photon interaction. We do this by making use of the fact that the
    mean-field dynamics are exact in the thermodynamic limit thanks to a uniform
    coupling between atoms and photons. We find ordered states with symmetry-broken
    components of the photon field and atomic excitation driven by the external
    field. The mechanism by which these ordered states arise is discussed from the
    viewpoint of the quantum interference effect.

    DOI

    Scopus

    16
    Citation
    (Scopus)

▼display all

Books and Other Publications

  • 量子技術の実用化と研究開発業務への導入方法

    多数( Part: Joint author, 第8章4節)

    技術情報協会  2023.01

  • 弱点克服 大学生の熱力学

    田中 宗, 轟木 義一, 田村 亮, 白井 達彦, 所 裕子( Part: Joint author, 第5章,第6章)

    東京図書(株)  2022.11 ISBN: 4489023715

Research Projects

  • 非平衡量子開放系における物性制御法の開発

    日本学術振興会  科学研究費助成事業

    Project Year :

    2023.04
    -
    2027.03
     

    白井 達彦

  • High Performance Computing for Materials Simulation by Quantum-Classical Hybrid Algorithms

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2021.04
    -
    2024.03
     

  • 非平衡定常状態の典型的な状態を用いた解析手法の構築

    日本学術振興会  科学研究費助成事業 若手研究

    Project Year :

    2018.04
    -
    2021.03
     

    白井 達彦

     View Summary

    量子統計力学を特徴付ける上で導入された典型的な状態は、孤立系での量子多体系において平衡状態の特徴づけや熱平衡化の問題を考える上で有用な概念として成功を収めている。本研究ではこの典型的な状態の概念を開放系に拡張することを目的に研究を進めている。
    本年度は特に非平衡環境と弱く接した系の定常状態に注目して研究を行った。このような系は急速に実験技術の進展を示すイオントラップ系や冷却原子系において実現し、近年理論研究も含め活発な研究対象となっている。本年度行なった研究によって、そのような非平衡環境にあるマクロな量子系の定常状態を記述する上で、固有状態熱化仮説が重要な役割を果たすことが明らかになった。より具体的には、系と散逸環境との間の相互作用の強さに関する摂動論が熱力学的極限においても妥当であるかを議論した。定常状態に保存カレントが流れていない場合には、摂動展開が漸近展開のように振る舞い、したがって摂動論が妥当であることを数値的に明らかにした。その結果、非平衡環境と接しており詳細釣合い条件が破れているにも関わらず、固有状態熱化仮説によって、ある有効温度の熱平衡状態がその定常状態の良い記述を与えることが分かった。一方で、異なる温度の散逸環境が接しているなど、バルクに定常カレントが流れている場合には、摂動論が破綻し、したがって定常状態は熱平衡状態として記述できないことも数値的に明らかにした。この結果は論文にまとめ、現在投稿中である。

  • 光子と物質の相互作用と周期外場の相乗効果で起こる非平衡相転移の研究

    日本学術振興会  科学研究費助成事業 特別研究員奨励費

    Project Year :

    2013.04
    -
    2016.03
     

    白井 達彦

     View Summary

    時間周期外場の下での量子統計力学をテーマとし研究を進めた。有限の強さの振動外場の下では、共鳴現象などの多彩な量子ダイナミクスが現れ、その制御手法としてフロケ演算子を用いた解析手法などが確立している。特に、最近では、フロケの擬固有値を実効的に固有値とみなすことによって、外場なしでは実現の難しいハミルトニアンを時間周期外場によって創り出すといったフロケエンジニアリングと呼ばれる研究が盛んに行われている。
    本年度は、このフロケの擬固有値スペクトルがどのような時に熱力学的な意味を持つかについて研究を行った。つまり、外場で制御したい注目系が、ある温度の熱的環境と接している状況を考え、その定常状態の分布関数がどのような条件の下で、注目系の擬固有値スペクトルと熱的環境の温度で特徴づけられるカノニカル分布になるかについて調べた。そして、明らかになった結果を論文にまとめた。さらに、この条件が満たされない場合についても調べ、新奇な動的相転移が起こることを発見し、研究発表を行った。
    この研究によって、ある条件の下では、熱的環境への散逸と時間周期外場による励起とのバランスにより実現する非平衡定常状態の分布関数とフロケの擬固有値との間に定量的な関係のあることが明らかになった。時間周期外場によって新奇な物性開発をするにあたって、定常状態の分布関数は重要な役割を担っている。その定常状態の分布関数が、熱浴の詳細によらない注目系のフロケの擬固有値によって特徴づけられるパラメータ領域があることを示した点に、本研究の意義がある。

Misc

  • Multi-spin flip method for an Ising machine

    白井達彦, 戸川望

    日本物理学会講演概要集(CD-ROM)   77 ( 1 )  2022

    J-GLOBAL

  • 9pAP-8 Periodically driven steady states independent of the structures of its thermal bath

    Shirai T., Mori T., Miyashita S.

    Meeting abstracts of the Physical Society of Japan   69 ( 2 ) 165 - 165  2014.08

    CiNii

  • 30pBD-6 Treatment of dissipation effects in a driven quantum open system

    Shirai T., Mori T., Miyashita S.

    Meeting abstracts of the Physical Society of Japan   69 ( 1 ) 385 - 385  2014.03

    CiNii

  • 29aXH-7 Phase transitions induced by AC external field and interaction

    Shirai Tatsuhiko, Mori Takashi, Miyashita Seiji

    Meeting abstracts of the Physical Society of Japan   68 ( 1 ) 397 - 397  2013.03

    CiNii

  • 18aAE-1 Phase transitions in the cavity system under an external field

    Shirai T., Mori T., Miyashita S.

    Meeting abstracts of the Physical Society of Japan   67 ( 2 ) 225 - 225  2012.08

    CiNii

  • 26pBE-2 Phase transitions in equilibrium and Non-equilibrium of the Tavis-Cummings model under an exteranal driving force

    Meeting abstracts of the Physical Society of Japan   67 ( 1 ) 218 - 218  2012.03

    CiNii

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Industrial Property Rights

  • 計算方法,計算システム,及びプログラム

    白井達彦, 戸川望

    Patent

  • 計算方法,計算システム,及びプログラム

    白井達彦, 戸川望

    Patent

  • 量子計算方法、量子計算システム、及びプログラム

    白井達彦,戸川望

    Patent

 

Syllabus

Teaching Experience

  • Javaプログラミング

    2020.10
    -
    Now
     

  • Cアプリケーションデベロップメント

    2020.04
    -
    Now
     

  • 理工学基礎実験

    2020.04
    -
     
     

 

Internal Special Research Projects

  • イジング計算機向けソフトウェアの開発

    2022  

     View Summary

    組合せ最適化問題を高速・高精度に解法すると期待されている量子アニーリングマシンやゲート型量子計算機を含めたイジング計算機の性能を改善するための理論研究を行った.前年度に開発した,単スピンフリップを動作原理とするイジング計算機においてマルチスピンフリップと等価な状態遷移を可能にするマージ手法を具体的な組合せ最適化問題に適用した結果をまとめ,論文としてIEEE Transactions on Computersに出版した.また,線形制約をもつ組合せ最適化問題を効率的かつ高精度に解くための手法としてスピン変数消去法を開発した.その結果は,日本物理学会2021年秋季大会で発表し,IEEE Transactions on Computersに出版した.

  • 量子計算物理学に向けた量子アルゴリズム開発

    2021  

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    量子効果を用いて組合せ最適化問題を解法する量子アニーリングについての理論研究を行なった。前年度行なった、ランダム横磁場イジング模型の量子相転移の動的臨界指数について、より広いクラスに対し解析的な結果を得た。その結果は、日本物理学会2021年秋季大会、AQC2021で発表し、論文としてAnnals of Physicsに出版した。 また、組合せ最適化問題を効率よく解法する可能性をもつイジング計算機に関する研究を行なった。単スピンフリップを動作原理とするイジング計算機においてマルチスピンフリップと等価な状態遷移を可能にするマージ手法を構築した。その結果は、情報処理学会(IPSJ-SLDM)、日本物理学会第77回年次大会で発表し、論文としてIEEE Transactions on Computersに投稿した。

  • 量子計算物理学に向けた量子アルゴリズム開発

    2020   戸川望, 田中宗

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    量子近似最適化アルゴリズムは、近未来的に実現する誤り訂正のできない量子コンピュータにおいて、量子超越性を示す一つの候補として注目されている。本研究では、最大カット問題と呼ばれる組合せ最適化問題に対する、量子近似最適化アルゴリズムの性能を調べた。2正則グラフの最大カット問題に対し、緩和問題を構成することで、量子近似最適化アルゴリズムの最適化問題が線形計画問題に帰着することを示した。緩和問題である線形計画問題を厳密に解くことで、量子近似最適化アルゴリズムの性能の上限を明らかにした。本研究の結果は、第二回量子ソフトウェア研究会で口頭発表した。