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Information-Theoretical Study of Entanglement and Geometry in Quantum Systems

Research Project

Project/Area Number 18K03474
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
Research InstitutionTohoku University (2020)
Sendai National College of Technology (2018-2019)

Principal Investigator

MATSUEDA Hiroaki  東北大学, 工学研究科, 教授 (20396518)

Project Period (FY) 2018-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsエンタングルメント / 情報幾何学 / 量子古典変換 / ホログラフィー原理 / くりこみ群 / 特異値分解 / テンソルネットワーク / スピン相関行列 / 情報幾何 / 量子エンタングルメント / ホログラフィー / ウェーブレット
Outline of Final Research Achievements

The duality (holographic principle) between quantum critical systems and classical general relativity is a very basic research subject that includes common issues in various physical fields. The main purpose of this research is to clarify this background from cross-disciplinary perspectives such as information geometry, mathematical physics, and condensed matter physics. To achieve this, I conducted research on two specific issues:(1) research to the functionality of singular value decomposition and holographic principles, and (2) construction of quantum classical correspondence by information geometry. In particular, regarding (1), it was found that the wave function can be restored and inferred from the singular value decomposition (principal component analysis) of the family information of the correlation function of the quantum system, and it is found that this result can contribute to the understanding of the mechanism of the quantum classical correspondence.

Academic Significance and Societal Importance of the Research Achievements

情報に関わる研究は現代の最重要テーマの一つである.AIや深層学習は現代技術社会における必須の技術であり,また量子コンピュータは国家的な戦略課題でもある.それと並行して,基礎科学の大きな革新である次世代物理学の構築にも量子情報理論の観点は本質的な役割を果たすと考えられている.本研究は極めて数理物理的な基礎研究ではあるものの,このような非常に広い視点から後者に貢献すべき堅実な研究成果であり,そこに学術的・社会的意義があると考えられる.

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (12 results)

All 2021 2020 2019 2018

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Open Access: 1 results) Presentation (10 results) (of which Int'l Joint Research: 2 results,  Invited: 4 results)

  • [Journal Article] Quantum Singular Value Decomposition of Spin Correlation Matrix in One-Dimensional Heisenberg Model2021

    • Author(s)
      Kohei Ohgane, Tatsuya Kumamoto, Hiroaki Matsueda
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 90 Issue: 5 Pages: 054001-054001

    • DOI

      10.7566/jpsj.90.054001

    • NAID

      40022563504

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Image-processing the topological charge density in the CP(N-1) model2020

    • Author(s)
      Yuya Abe, Kenji Fukushima, Yoshimasa Hidaka, Hirokai Matsueda, Koichi Murase, Shoichi Sasaki
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: 013D02 Issue: 1 Pages: 1-19

    • DOI

      10.1093/ptep/ptz134

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Information-Theoretical Approaches to Measurement and Control of Novel Quantum Excitations in Condensed Matter2021

    • Author(s)
      松枝宏明
    • Organizer
      第62回黎明研究会
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] 環境及び励起光と結合した量子ビット系に対するエンタングルメントによる固有状態の分類2021

    • Author(s)
      松枝宏明,井出恕也,石田邦夫
    • Organizer
      日本物理学会第75回年次大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] ゲージ重力対応の情報幾何学的研究-古典座標の量子対応物に関する検討-2020

    • Author(s)
      松枝宏明
    • Organizer
      日本物理学会2020年秋季大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 特異値分解とウェーブレット変換の比較2020

    • Author(s)
      松枝宏明,森知生,佐藤健太郎
    • Organizer
      日本物理学会第75回年次大会
    • Related Report
      2019 Research-status Report
  • [Presentation] トポロジカル秩序を持つ系の特異値分解による解析2019

    • Author(s)
      松枝宏明
    • Organizer
      日本物理学会2019年秋季大会
    • Related Report
      2019 Research-status Report
  • [Presentation] Singular Value Decomposition & Information Geometry - Information-Theoretical Approaches to Interdisciplinary Physics Research -2018

    • Author(s)
      Hiroaki Matsueda
    • Organizer
      KITS Workshop on "Electron correlation, Quantum Biology and Quantum Information", KITS Beiging
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] ホログラフィック原理と情報幾何・エンタングルメント2018

    • Author(s)
      松枝宏明
    • Organizer
      東大物性研研究会「量子情報・物性の新潮流-量子技術が生み出す多様な物性と情報処理技術-」
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Singular-Value-Decomposition Study of Holography and Renormalization2018

    • Author(s)
      Hiroaki Matsueda
    • Organizer
      International Conference on Holography, String Theory and discrete Approaches in Hanoi, Institute of Physics, VAST, Hanoi, Vietnam
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Lieb-Liniger模型におけるベーテ仮説と複合励起2018

    • Author(s)
      及川達希,松枝宏明
    • Organizer
      日本物理学会秋季大会,同志社大学京田辺キャンパス
    • Related Report
      2018 Research-status Report
  • [Presentation] 1次元自由電子系のエンタングルメントスペクトルに対するヘッセ幾何学(Ⅱ)2018

    • Author(s)
      松枝宏明
    • Organizer
      日本物理学会秋季大会,同志社大学京田辺キャンパス
    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2022-01-27  

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