Details of the Researcher

PHOTO

Manaka Okuyama
Section
Graduate School of Information Sciences
Job title
Assistant Professor
Degree

  • 博士（理学）（東京工業大学）

  • 修士（理学）（東京工業大学）

Research History 2

  • 2019/04 - Present
    Tohoku University

  • 2017/04 - 2019/03
    Tokyo Institute of Technology　School of Science

Education 3

  • Tokyo Institute of Technology　School of Science

    2017/04 - 2019/03

  • Tokyo Institute of Technology　Science of Engineering　Condensed Matter Physics

    2015/04 - 2017/03

  • Tokyo Institute of Technology　School of Science　Dept. of Physics

    2011/04 - 2015/03

Professional Memberships 1

  • THE PHYSICAL SOCIETY OF JAPAN

Research Areas 1

  • Natural sciences / Mathematical physics and basic theory /

Papers 20

  1. Temperature chaos as a logical consequence of the reentrant transition in spin glasses

    Hidetoshi Nishimori, Masayuki Ohzeki, Manaka Okuyama

    Physical Review E　112　(4)　2025/10/22

    Publisher: American Physical Society (APS)

    DOI： 10.1103/qp1w-qcbs 　

    ISSN： 2470-0045

    eISSN： 2470-0053

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    Temperature chaos is a striking phenomenon in spin glasses, where even slight changes in temperature lead to a complete reconfiguration of the spin state. Another intriguing effect is the reentrant transition, in which lowering the temperature drives the system from a ferromagnetic phase into a less ordered spin-glass or paramagnetic phase. In the present paper, we reveal an unexpected connection between these seemingly unrelated phenomena in the finite-dimensional Edwards-Anderson model of spin glasses by introducing a generalized formulation that incorporates correlations among disorder variables. Assuming the existence of a spin-glass phase at finite temperature, we establish that temperature chaos arises as a logical consequence of reentrance in the Edwards-Anderson model. Our findings uncover a previously hidden mathematical structure relating reentrance and temperature chaos, offering a new perspective on the physics of spin glasses beyond the mean-field theory.

  2. Free energy equivalence between mean-field models and nonsparsely diluted mean-field models Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of Physics A: Mathematical and Theoretical　58　(4)　045004-045004　2025/01/24

    Publisher: IOP Publishing

    DOI： 10.1088/1751-8121/adaab4 　

    ISSN： 1751-8113

    eISSN： 1751-8121

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    Abstract We studied nonsparsely diluted mean-field models that differ from sparsely diluted mean-field models, such as the Viana–Bray model. When the existence probability of each edge follows a Bernoulli distribution, we rigorously prove that the free energy of nonsparsely diluted mean-field models with appropriate parameterization coincides exactly with that of the corresponding mean-field models in ferromagnetic and spin-glass models composed of any discrete spin S in the thermodynamic limit. Our results is a broad generalization of the result of a previous study (Bovier and Gayrard 1993 J. Stat. Phys. 72 643), where the densely diluted mean-field ferromagnetic Ising model (diluted Curie–Weiss model) with appropriate parameterization was analyzed rigorously, and it was proven that its free energy was exactly equivalent to that of the corresponding mean-field model (Curie–Weiss model).

  3. Existence of Long-Range Order in Random-Field Ising Model on Dyson Hierarchical Lattice Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of Statistical Physics　192　(2)　2025/01/22

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s10955-025-03399-9 　

    eISSN： 1572-9613

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    Abstract We study the random-field Ising model on a Dyson hierarchical lattice, where the interactions decay in a power-law-like form, $$J(r)\sim r^{-\alpha }$$ , with respect to the distance. Without a random field, the Ising model on the Dyson hierarchical lattice has a long-range order at finite low temperatures when $$1<\alpha <2$$ . In this study, for $$1<\alpha <3/2$$ , we rigorously prove that there is a long-range order in the random-field Ising model on the Dyson hierarchical lattice at finite low temperatures, including zero temperature, when the strength of the random field is sufficiently small but nonzero. Our proof is based on Dyson’s method for the case without a random field, and the concentration inequalities in probability theory enable us to evaluate the effect of a random field.

  4. Replica bound for Ising spin glass models in one dimension Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of Physics A: Mathematical and Theoretical　58　(1)　015003-015003　2024/12/11

    Publisher: IOP Publishing

    DOI： 10.1088/1751-8121/ad97fb 　

    ISSN： 1751-8113

    eISSN： 1751-8121

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    Abstract The interpolation method is a powerful tool for rigorous analysis of mean-field spin glass models, both with and without dilution. In this study, we show that the interpolation method can be applied to Ising spin glass models in one dimension, such as a one-dimensional chain and a two-leg ladder. In one dimension, the replica symmetric (RS) cavity method is naturally expected to be rigorous for Ising spin glass models. Using the interpolation method, we rigorously prove that the RS cavity method provides lower bounds on the quenched free energies of Ising spin glass models in one dimension at any finite temperature in the thermodynamic limit.

  5. Toward Mean-Field Bound for Critical Temperature on Nishimori Line Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of the Physical Society of Japan　93　(10)　2024/10/15

    Publisher: Physical Society of Japan

    DOI： 10.7566/jpsj.93.104706 　

    ISSN： 0031-9015

    eISSN： 1347-4073

  6. Exact Solution of Free Entropy for Matrix-Valued Geometric Brownian Motion with Non-Commutative Matrices via Replica Method Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of the Physical Society of Japan　92　(11)　2023/11/15

    Publisher: Physical Society of Japan

    DOI： 10.7566/jpsj.92.114001 　

    ISSN： 0031-9015

    eISSN： 1347-4073

  7. Gibbs–Bogoliubov Inequality on the Nishimori Line Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of the Physical Society of Japan　92　(8)　2023/08/15

    Publisher: Physical Society of Japan

    DOI： 10.7566/jpsj.92.084002 　

    ISSN： 0031-9015

    eISSN： 1347-4073

  8. Mean-field theory is exact for Ising spin glass models with Kac potential in non-additive limit on Nishimori line Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of Physics A: Mathematical and Theoretical　56　(32)　325003-325003　2023/07/24

    Publisher: IOP Publishing

    DOI： 10.1088/1751-8121/ace6e4 　

    ISSN： 1751-8113

    eISSN： 1751-8121

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    Abstract Recently, Mori (2011 Phys. Rev. E 84 031128) has conjectured that the free energy of Ising spin glass models with the Kac potential in the non-additive limit, such as the power-law potential in the non-additive regime, is exactly equal to that of the Sherrington–Kirkpatrick model in the thermodynamic limit. In this study, we prove that his conjecture is true on the Nishimori line at any temperature in any dimension. One of the key ingredients of the proof is the use of the Gibbs–Bogoliubov inequality on the Nishimori line. We also consider the case in which the probability distribution of the interaction is symmetric, where his conjecture is true at any temperature in one dimension but is an open problem in the low-temperature regime in two or more dimensions.

  9. Threshold theorem in isolated quantum dynamics with stochastic control errors Invited Peer-reviewed

    Manaka Okuyama, Kentaro Ohki, Masayuki Ohzeki

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences　381　20210412　2022/12/05

    DOI： 10.1098/rsta.2021.0412 　

  10. Inequality for Local Energy of Ising Model with Quenched Randomness and Its Application Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of the Physical Society of Japan　89　(6)　064704-064704　2020/06/15

    Publisher: Physical Society of Japan

    DOI： 10.7566/jpsj.89.064704 　

    ISSN： 0031-9015

    eISSN： 1347-4073

  11. Upper bound on the second derivative of the quenched pressure in spin-glass models: weak Griffiths second inequality

    Manaka Okuyama, Masayuki Ohzeki

    2020/05/14

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    The Griffiths first and second inequalities have played an important role in the analysis of ferromagnetic models. In spin-glass models, although the counterpart of the Griffiths first inequality has been obtained, the counterpart of the Griffiths second inequality has not been established. In this study, we generalize the method in the previous work [J. Phys. Soc. Jpn. 76, 074711 (2007)] to the case with multi variables for both symmetric and non-symmetric distributions of the interactions, and derive some correlation inequalities for spin-glass models. Furthermore, by combining the acquired equalities in symmetric distributions, we show that there is a non-trivial positive upper bound on the second derivative of the quenched pressure with respect to the strength of the randomness, which is a weak result of the counterpart of the Griffiths second inequality in spin-glass models for general symmetric distributions.

  12. Some inequalities for correlation functions of Ising models with quenched randomness

    Manaka Okuyama, Masayuki Ohzeki

    2020/04/13

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    Correlation inequalities have played an essential role in the analysis of ferromagnetic models but have not been established in spin glass models. In this study, we obtain some correlation inequalities for the Ising models with quenched randomness, where the distribution of the interactions is symmetric. The acquired inequalities can be regarded as an extension of the previous results, which were limited to the local energy for a spin set, to the local energy for a pair of spin sets. Besides, we also obtain some correlation inequalities for asymmetric distribution.

  13. An exact solution of the partition function for mean-field quantum spin systems without the static approximation

    Manaka Okuyama, Masayuki Ohzeki

    arXiv　2018/08

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    Suzuki-Trotter decomposition is a well-known technique used to calculate the<br /> partition function of quantum spin systems, in which the imaginary-time<br /> dependence of the partition function occurs inevitably. Since it is very<br /> difficult to explicitly treat the imaginary-time dependence of the partition<br /> function, we usually neglect the imaginary-time dynamical effect, which is<br /> called the static approximation. Although the static approximation is the first<br /> approach, it is not even clear when the static approximation is justified for<br /> mean-field quantum spin systems, that is, mean-field quantum spin systems have<br /> not been solved exactly so far. In this study, we solve exactly the partition<br /> function for a particular class of mean-field quantum spin systems including<br /> randomness without the static approximation. The partition function can be<br /> regarded as a result of time evolution in the imaginary-time Schr\&quot;odinger<br /> equation, and solving the exact solution of the partition function is<br /> equivalent to solving the optimal control problem in the imaginary-time<br /> Schr\&quot;odinger equation. As the result, the solution of the optimal control<br /> problem coincides exactly with the static approximate solution of the partition<br /> function and, therefore, the static approximation is exact for the particular<br /> class of mean-field quantum spin systems including randomness in general.<br /> Furthermore, we prove that the analysis of the previous study in quantum<br /> annealing is exact where the non-stoquastic interaction and the inhomogeneous<br /> transverse field accelerate the computational time exponentially for mean-field<br /> quantum spin systems.

  14. Comment on ‘Energy-time uncertainty relation for driven quantum systems’ Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Journal of Physics A: Mathematical and Theoretical　2018/08

    Publisher: {IOP} Publishing

    DOI： 10.1088/1751-8121/aacb90 　

  15. A useful fundamental speed limit for the imaginary-time Schrodinger equation

    Manaka Okuyama, Masayuki Ohzeki

    2018/06

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    The quantum speed limit (QSL), or the energy-time uncertainty relation, gives<br /> a fundamental speed limit for quantum dynamics. Recently, Kieu<br /> [arXiv:1702.00603] derived a new class of QSL which is not only formal but also<br /> suitable for actually evaluating the speed limit. Inspired by his work, we<br /> obtain a similar speed limit for the imaginary-time Schr\&quot;odinger equation.<br /> Using this new bound, we show that the optimal computational time of the Grover<br /> problem in imaginary-time quantum annealing is bounded from below by $\log N$,<br /> which is consistent with a result of previous study.

  16. Quantum Speed Limit is Not Quantum Peer-reviewed

    Manaka Okuyama, Masayuki Ohzeki

    Physical Review Letters　120　(7)　2018/02/12

    Publisher: American Physical Society

    DOI： 10.1103/PhysRevLett.120.070402 　

    ISSN： 1079-7114 0031-9007

  17. Comment on "Energy-time uncertainty relation for driven quantum systems" and "Quantum Speed Limit for Non-Markovian Dynamics"

    Manaka Okuyama, Ryo Takahashi, Masayuki Ohzeki

    arXiv　2018/02

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    Deffner and Lutz [J. Phys. A 46, 335302 (2013) and Phys. Rev. Lett. 111,<br /> 010402 (2013).] extended the Mandelstam-Tamm bound and the Margolus-Levitin<br /> bound to time-dependent and non-Markovian systems, respectively. Although the<br /> derivation of the Mandelstam-Tamm bound is correct, we point out that thier<br /> analysis of the Margolus-Levitin bound is incorrect. The Margolus-Levitin bound<br /> has not yet been established in time-dependent quantum systems, except for the<br /> adiabatic case.

  18. Quantum-Classical Correspondence of Shortcuts to Adiabaticity Peer-reviewed

    Manaka Okuyama, Kazutaka Takahashi

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN　86　(4)　2017/04

    DOI： 10.7566/JPSJ.86.043002 　

    ISSN： 0031-9015

  19. From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity Peer-reviewed

    Manaka Okuyama, Kazutaka Takahashi

    PHYSICAL REVIEW LETTERS　117　(7)　2016/08

    DOI： 10.1103/PhysRevLett.117.070401 　

    ISSN： 0031-9007

    eISSN： 1079-7114

  20. Anomalous behavior of the energy gap in the one-dimensional quantum XY model Peer-reviewed

    Manaka Okuyama, Yuuki Yamanaka, Hidetoshi Nishimori, Marek M. Rams

    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics　92　(5)　2015/11/13

    Publisher: American Physical Society

    DOI： 10.1103/PhysRevE.92.052116 　

    ISSN： 1550-2376 1539-3755

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Research Projects 6

  1. Toward rigorous analysis of finite-dimensional spin glass models on the Nishimori line

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Early-Career Scientists

    Institution: Tohoku University

    2024/04/01 - 2029/03/31

  2. Realizations and practical applications of quantum statistical machine learning theory with navigation functions

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2022/04/01 - 2025/03/31

  3. Realizations and practical applications of quantum statistical machine learning theory with navigation functions

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2022/04/01 - 2025/03/31

  4. 確率的な制御誤差が量子アニーリングの性能に与える影響の評価

    奥山 真佳

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 若手研究

    Institution: 東北大学

    2021/04/01 - 2024/03/31

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    量子アニーリングは孤立量子系の時間発展を計算に利用する量子計算方式の一種である。孤立量子系の時間発展は理想的にはシュレディンガー方程式によって記述されるが、現実の実験系では外界の影響を完全に排除することは難しい。外界が孤立量子系に与える影響として、これまでの先行研究では熱浴との相互作用や決定論的に生じるハミ ルトニアンの制御誤差のみが議論されてきた。しかしながら、ハミルトニアンの制御誤差には、決定論的に生じる誤差だけでなく、確率的に生じる誤差も存在する。そこで、本研究課題ではハミルトニアンに確率的に生じる制御誤差をシュレディンガー方程式における確率ノイズとして定式化することにより、確率微分方程式の解析を通じて、確率的な制御誤差が量子アニーリングの効率にどのような影響を及ぼすかを解明する。 本年度は二つの方針で研究課題に取り組んだ。一つ目の方針は確率微分方程式において断熱定理を確立することである。断熱定理は断熱量子計算の性能評価の基礎となるものであり、ゆっくりと状態を時間発展させれば系の状態が常に基底状態そって変化することを意味する。断熱定理は量子アニーリングの性能評価においてもしばしば用いられるものであり、確率的な制御誤差が存在する場合に断熱定理を拡張することは本研究課題の目的のために非常に重要である。先行研究では確率ノイズが決定的な項と可換な場合に断熱定理の対応物が得られている。先行研究の結果を非可換な場合に拡張するべく取り組んでいるが、残念ながら満足のいく結果は得られていない。 二つ目の方針は量子多体系の時間発展に確率的な制御誤差が与える影響を調べることである。特に、本年度は確率的な制御誤差が動的量子相転移に与える影響について詳しく解析を行った。解析計算の結果、申請者の問題設定の範囲では確率的な制御誤差が動的量子相転移の性質に大きな影響を与えないことが明らかとなった。

  5. Optimal control theory solves spin glass models with transverse field

    Okuyama Manaka

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Research Activity Start-up

    Institution: Tohoku University

    2019/08/30 - 2022/03/31

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    In this study, a new quantum mean-field spin glass model, which is expected to have an analytically rigorous treatment, is introduced using stochastic differential equations and studied analytically. We construct a replica symmetric solution using the replica method and confirm that it is consistent with the results of the Approximate Message Passing algorithm for stochastic differential equations.

  6. 有限時間における量子アニーリングの性能評価

    奥山 真佳

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 特別研究員奨励費

    Institution: 東京工業大学

    2017/04 - 2020/03

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    どのような量子揺らぎが量子アニーリングの計算時間を改善するかを明らかにするために、先行研究では平均場量子スピン系の相転移の解析がしばしば行われている。研究課題の二年目では平均場量子スピン系の解析において広く用いられている静的近似の厳密性に関する研究を集中的に行った。 静的近似は鈴木・トロッター変換によって量子系の分配関数を計算する際、秩序パラメータの虚時間依存性を無視する近似である。静的近似は必ずしも良い近似解を与えるわけではなく、ランダム性の強い横磁場SK模型では静的近似が破綻することが知られている。一方で、相互作用が一様な平均場模型では解析計算、数値計算の結果などから静的近似が厳密であると信じられていたが、その証明は与えられていなかった。量子アニーリングの先行研究においても静的近似は頻繁に用いられており、その厳密性を調べることは量子アニーリングの性能評価を行う上で重要である。 申請者は有限パターンのHopfield模型を一般化したクラスの平均場量子スピン系に対して、分配関数の虚時間依存性を厳密に扱う問題を虚時間シュレディンガー方程式における最適制御問題と見做すことにより、熱力学極限で分配関数を厳密に求めた。結果として、このクラスの平均場量子スピン系では静的近似が常に厳密であることが明らかになった。我々の模型は量子アニーリングの先行研究において扱われた平均場量子スピン系の多くを含んでおり、それらの結果が厳密であることを意味する。以上の結果は論文として現在投稿中である。 <BR> また、前年度に引き続き、量子速度限界に関する研究も行った。先行研究において量子アニーリングにおけるGrover問題の最適性を示すために用いられた不等式を虚時間シュレディンガー方程式に対して拡張し、虚時間量子アニーリングにおけるGrover問題の最適性を示すことに成功した。以上の結果は論文として現在投稿中である。

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