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optimal control of dynamical quantum systems

Research Project

Project/Area Number 26400385
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionTokyo Institute of Technology

Principal Investigator

Takahashi Kazutaka  東京工業大学, 理学院, 助教 (70415214)

Project Period (FY) 2014-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords断熱状態制御の方法 / 量子アニーリング / 断熱状態 / 動的相転移 / ゆらぎの定理 / エントロピー / 情報幾何学 / ソリトン / Landau-Zener遷移 / KdV方程式 / 量子クエンチ / 量子古典対応 / Markov過程 / 詳細つりあい条件の破れ / 戸田方程式 / 量子最速曲線 / 動的特異性
Outline of Final Research Achievements

“Shortcuts to adiabaticity“ is known as a method accelerating adiabatic dynamics. I found, after studying many applications, that the method is very general and can be applied to any dynamical systems including quantum, classical, and statistical systems. The Hamiltonian of the system is separated into two parts, and each can be interpreted as the energy of the system and the generator of the time evolution.
As one of the main achievement, we found that the Lax formalism for classical nonlinear integrable systems is shown to be equivalent to shortcuts to adiabaticity. This equivalence gives nontrivial solutions of quantum and classical dynamics. The most important point is that we found not only specific solutions but also several series of solutions exhaustively.

Academic Significance and Societal Importance of the Research Achievements

動力学の問題を解くことは一般に難しいが、本研究によって統一的な見方が得られた。当初は制御の問題を想定して研究を行っていたが、必ずしもそれに限らない描像を得たことは意義が大きい。動力学を理解する端緒となることが期待される。
また、これも想定外であったが、本研究の成果は量子力学に限らず古典力学や統計力学の系にも適用ができる。今後は本研究で得られた描像に立ってさまざまな系の動的な性質や制御問題を調べるという研究が行われることを期待している。

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (29 results)

All 2019 2018 2017 2016 2015 2014 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results,  Open Access: 2 results,  Acknowledgement Compliant: 5 results) Presentation (18 results) (of which Int'l Joint Research: 8 results,  Invited: 11 results) Remarks (1 results)

  • [Journal Article] Hamiltonian Engineering for Adiabatic Quantum Computation: Lessons from Shortcuts to Adiabaticity2019

    • Author(s)
      Kazutaka Takahashi
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 88 Issue: 6 Pages: 061002-061002

    • DOI

      10.7566/jpsj.88.061002

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Counterdiabatic Hamiltonians for multistate Landau-Zener problem2018

    • Author(s)
      Nishimura Kohji、Takahashi Kazutaka
    • Journal Title

      SciPost Physics

      Volume: 5 Issue: 3 Pages: 29-29

    • DOI

      10.21468/scipostphys.5.3.029

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions2017

    • Author(s)
      Obuchi Tomoyuki、Suzuki Sei、Takahashi Kazutaka
    • Journal Title

      Physical Review B

      Volume: 95 Issue: 17 Pages: 174305-174305

    • DOI

      10.1103/physrevb.95.174305

    • NAID

      130007507829

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Shortcuts to adiabaticity applied to nonequilibrium entropy production: an information geometry viewpoint2017

    • Author(s)
      Takahashi Kazutaka
    • Journal Title

      New Journal of Physics

      Volume: 19 Issue: 11 Pages: 115007-115007

    • DOI

      10.1088/1367-2630/aa9534

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quantum-classical correspondence of shortcuts to adiabaticity2017

    • Author(s)
      Manaka Okuyama and Kazutaka Takahashi
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 86 Issue: 4 Pages: 043002-043002

    • DOI

      10.7566/jpsj.86.043002

    • NAID

      210000134319

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] From classical nonlinear integrable systems to quantum shortcuts to adiabaticity2016

    • Author(s)
      Manaka Okuyama and Kazutaka Takahashi
    • Journal Title

      Physical Review Letters

      Volume: 117 Issue: 7 Pages: 070401-070401

    • DOI

      10.1103/physrevlett.117.070401

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Shortcuts to adiabaticity for quantum annealing2016

    • Author(s)
      Kazutaka Takahashi
    • Journal Title

      Physical Review A

      Volume: 95 Issue: 1 Pages: 012309-012309

    • DOI

      10.1103/physreva.95.012309

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Conflict between fastest relaxation of a Markov process and detailed balance condition2016

    • Author(s)
      Kazutaka Takahashi and Masayuki Ohzeki
    • Journal Title

      Physical Review E

      Volume: 93 Issue: 1

    • DOI

      10.1103/physreve.93.012129

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Unitary deformations of counterdiabatic driving2015

    • Author(s)
      Kazutaka Takahashi
    • Journal Title

      Physical Review A

      Volume: 91 Issue: 4

    • DOI

      10.1103/physreva.91.042115

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Fast-forward scaling in a finite-dimensional Hilbert space2014

    • Author(s)
      Kazutaka Takahashi
    • Journal Title

      Physical Review A

      Volume: 89 Issue: 4

    • DOI

      10.1103/physreva.89.042113

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] 制御の問題から見る動力学の普遍的構造2018

    • Author(s)
      高橋和孝
    • Organizer
      非平衡系の物理学-階層性と普遍性-
    • Related Report
      2018 Annual Research Report
  • [Presentation] Quantum-classical correspondence of shortcuts to adiabaticity2017

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      OIST workshop on quantum control
    • Place of Presentation
      OIST, Okinawa
    • Year and Date
      2017-03-21
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 断熱制御の方法と非平衡関係式2017

    • Author(s)
      高橋 和孝
    • Organizer
      日本物理学会2017年秋季大会
    • Related Report
      2017 Research-status Report
  • [Presentation] Structures of quantum, classical, and statistical dynamics2017

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      International workshop on quantum information, quantum computing and quantum control
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Hamiltonian engineering for many-body quantum systems by shortcuts to adiabaticity2016

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      Workshop on theory and practice of adiabatic quantum computers and quantum simulation
    • Place of Presentation
      ICTP, Trieste
    • Year and Date
      2016-08-22
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 量子断熱状態の制御とKdV方程式2016

    • Author(s)
      高橋 和孝, 奥山 真佳
    • Organizer
      日本物理学会第71回年次大会
    • Place of Presentation
      東北学院大学
    • Year and Date
      2016-03-19
    • Related Report
      2015 Research-status Report
  • [Presentation] Optimization of Markov process violates detailed balance condition2016

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      Topics in Advanced Monte Carlo Methods
    • Place of Presentation
      Institute of Statistical Mathematics
    • Year and Date
      2016-03-09
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Shortcuts to adiabaticity for nonlinear systems2016

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      Workshop on quantum control
    • Place of Presentation
      Kindai University
    • Year and Date
      2016-02-25
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimization of Markov process violates detailed balance condition2015

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      Breaking and beyond detailed balance condition-expanding to machine learning-
    • Place of Presentation
      Kyoto University
    • Year and Date
      2015-12-21
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] How to find shortcuts to adiabaticity2015

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      Uzbekistan workshop
    • Place of Presentation
      Uzbekistan National University
    • Year and Date
      2015-10-23
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Shortcuts to adiabaticity2015

    • Author(s)
      高橋 和孝
    • Organizer
      基研研究会「量子制御技術の発展により拓かれる量子情報の新時代」
    • Place of Presentation
      京都大学基礎物理学研究所
    • Year and Date
      2015-07-13
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] How to find shortcuts to adiabaticity2015

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      Adiabatic Quantum Computing
    • Place of Presentation
      ETH, Zurich
    • Year and Date
      2015-06-29
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Markov過程の最適化と詳細つりあいの破れ2015

    • Author(s)
      高橋 和孝
    • Organizer
      日本物理学会第70回年次大会
    • Place of Presentation
      早稲田大学(東京)
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Quantum Brachistochrone2015

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      OIST Mini Symposium: Quantum Control of Light and Matter
    • Place of Presentation
      沖縄科学技術大学院大学(恩納)
    • Year and Date
      2015-01-14 – 2015-01-16
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 量子O(N)模型における量子クエンチの動的特異性2014

    • Author(s)
      高橋 和孝
    • Organizer
      日本物理学会2014年秋季大会
    • Place of Presentation
      中部大学(春日井)
    • Year and Date
      2014-09-07 – 2014-09-10
    • Related Report
      2014 Research-status Report
  • [Presentation] How to find shortcuts to adiabaticity - Brachistochrone problem in quantum systems2014

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      YITP Workshop on Quantum Information Physics
    • Place of Presentation
      京都大学基礎物理学研究所(京都)
    • Year and Date
      2014-08-04 – 2014-08-07
    • Related Report
      2014 Research-status Report
  • [Presentation] How to find shortcuts to adiabaticity - Brachistochrone problem in quantum systems2014

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      Shortcuts to Adiabaticity 2014
    • Place of Presentation
      上海大学(上海)
    • Year and Date
      2014-07-01 – 2014-07-04
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Counterdiabatic driving from quantum brachistochrone equations2014

    • Author(s)
      Kazutaka Takahashi
    • Organizer
      Mini-workshop on real-time dynamics of quantum many-body systems
    • Place of Presentation
      東京大学(東京)
    • Year and Date
      2014-05-20
    • Related Report
      2014 Research-status Report
    • Invited
  • [Remarks]

    • URL

      http://www.stat.phys.titech.ac.jp/~ktaka/research.html

    • Related Report
      2016 Research-status Report

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Published: 2014-04-04   Modified: 2020-03-30  

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