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Quantum-Classical Correlation Games and New Analyses of Discrete-Continuous Optimization and Computational Complexity

Research Project

Project/Area Number 20300002
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionThe University of Tokyo

Principal Investigator

IMAI Hiroshi  The University of Tokyo, 大学院・情報理工学系研究科, 教授 (80183010)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥18,980,000 (Direct Cost: ¥14,600,000、Indirect Cost: ¥4,380,000)
Fiscal Year 2010: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2009: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2008: ¥7,150,000 (Direct Cost: ¥5,500,000、Indirect Cost: ¥1,650,000)
Keywords量子コンピュータ / 量子計算 / アルゴリズム / 量子情報 / 離散数学 / 量子エレクトロニクス / 計算機システム
Research Abstract

Quantum Computing overcomes the barriers of current classical computers through computational power via quantum effects. This research focuses on quantum correlation as such effects. We analyze quantum correlation in a unified way as follows : (1) revealing discrete aspects of quantum correlation by the theory of cut polytopes in combinatorial optimization, (2) investigating maximum quantum violations by continuous optimization, and (3) analyzing quantum correlation by multi-prover interactive proof in computational complexity theory. Furthermore, problems in new quantum computational models and quantum information are explored through discrete and continuous geometric structures.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (36 results)

All 2011 2010 2009 2008

All Journal Article (22 results) (of which Peer Reviewed: 20 results) Presentation (14 results)

  • [Journal Article] Voronoi Diagrams on Periodic Graphs.2010

    • Author(s)
      N.Fu, H.Imai, S.Moriyama
    • Journal Title

      Proceedings of 2010 International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2010)

      Pages: 189-198

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Revisiting Hyperbolic Voronoi Diagrams from Theoretical, Applied and Generalized Viewpoints.2010

    • Author(s)
      T.Tanuma, H.Imai, S.Moriyama
    • Journal Title

      Proceedings of 2010 International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2010)

      Pages: 23-32

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Voronoi Diagrams on Periodic Graphs.2010

    • Author(s)
      N.Fu, H.Imai, S.Moriyama
    • Journal Title

      Proceedings of 2010 International Symposium on Voronoi Diagrams in Science and Engineering

      Pages: 189-198

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Revisiting Hyperbolic Voronoi Diagrams from Theoretical, Applied and Generalized Viewpoints.2010

    • Author(s)
      T.Tanuma, H.Imai, S.Moriyama
    • Journal Title

      Proceedings of 2010 International Symposium on Voronoi Diagrams in Science and Engineering

      Pages: 23-32

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Deciding Non-Realizability of Oriented Matroids by Semidefinite Programming.2009

    • Author(s)
      H.Miyata, S.Moriyama, H.Imai
    • Journal Title

      Pacific Journal of Optimization Vol.5

      Pages: 211-224

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Deciding non-realizability of oriented matroids by semidefinite programming2009

    • Author(s)
      H.Miyata, S.Moriyama, H.Imai
    • Journal Title

      Pacific Journal of Optimization Vol.5

      Pages: 211-224

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Proximity and Bichromatic Matching on Planar Crystal Lattices2009

    • Author(s)
      N.Fu, H.Imai
    • Journal Title

      Optimization Days (企画講演)

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Generating Facets for the Cut Polytope of a Graph by Triangular Elimination.2008

    • Author(s)
      D.Avis, H.Imai, T.Ito
    • Journal Title

      Mathematical Programming Vol.112, No.2

      Pages: 303-325

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Shiftability of Atoms on a Lattice to Any Configuration in Minimum Moves.2008

    • Author(s)
      N.Fu, H.Imai
    • Journal Title

      Proceedings of the Japan-Korea Workshop on Algorithms and Computation (WAAC 2008)

      Pages: 28-35

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Computational Geometry Analysis of Quantum State Space and Its Applications2008

    • Author(s)
      K.Kato, M.Oto, H.Imai, K. Imai
    • Journal Title

      Generalized Voronoi Diagram : A Geometry-Based Approach to Computational Intelligence((M. L. Gavrilova, ed.), Springer)

      Pages: 67-108

    • Related Report
      2010 Final Research Report
  • [Journal Article] Smallest Enclosing Ball Problem in a Quantum State Space and Its Application.2008

    • Author(s)
      K.Kato, H.Imai, K. Imai
    • Journal Title

      Proceedings of the 5th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2008)

      Pages: 123-132

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Note on the Upper Bound Derived by Semidefinite Programming for the Maximum Quantum Violation of Bell Inequalities.2008

    • Author(s)
      T.Takahashi, S.Moriyama, H.Imai
    • Journal Title

      Proceedings of the 8th Asian Conference on Quantum Information Science Vol.1

      Pages: 127-128

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Solvability of Sliding Atoms Puzzle on a Lattice.2008

    • Author(s)
      N.Fu, H.Imai
    • Journal Title

      Proceedings of the 8th Asian Conference on Quantum Information Science

      Pages: 165-166

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analyzing Geometric Realizability Problems by Semidefinite Programming.2008

    • Author(s)
      H.Miyata, S.Moriyama, H.Imai
    • Journal Title

      Proceedings of the Kyoto RIMS Workshop on Computational Geometry and Discrete Mathematics

      Pages: 6-9

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Large Scale Matroid Enumeration and Analysis of Orientation.2008

    • Author(s)
      Y.Matsumoto, S.Moriayma, H.Imai, D.Bremner
    • Journal Title

      Proceedings of the Kyoto RIMS Workshop on Computational Geometry and Discrete Mathematics

      Pages: 10-13

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generating Facets for the Cut Polytope of a Graph by Triangular Elimination2008

    • Author(s)
      D. Avis, H. Imai and T. Ito
    • Journal Title

      Mathematical Programming Vol.122,No.2

      Pages: 303-325

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shiftability of Atoms on a Lattice to Any Configuration in Minimum Moves2008

    • Author(s)
      N. Fu and H. Imai
    • Journal Title

      Proceedings of the Japan-Korea Workshop on Algorithms and Computation (WAAC 2008) Vol.1

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Smallest enclosing ball problem in a quantum state space and its application2008

    • Author(s)
      K. Kato, H. Imai and K. Imai
    • Journal Title

      Proceedings of the 5th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD-2008) Vol.1

      Pages: 123-132

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Note on the Upper Bound Derived by Semidefinite Programming for the Maximum Quantum Violation of Bell Inequalities2008

    • Author(s)
      T. Toshiaki, S. Moriyama and H. Imai
    • Journal Title

      Proceedings of the 8th Asian Conference on Quantum Information Science, Poster Session A-9 Vol.1

      Pages: 127-128

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solvability of Sliding Atoms Puzzle on a Lattice2008

    • Author(s)
      N. Fu and H. Imai
    • Journal Title

      Proceedings of the 8th Asian Conference on Quantum Information Science Vol.1

      Pages: 165-166

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analyzing geometric realizability problems by semidefinite programming2008

    • Author(s)
      H. Miyata, S. Moriyama and H. Imai
    • Journal Title

      Proceedings of the Kyoto RIMS Workshop on Computational Geometry and Discrete Mathematics Vol.1

      Pages: 6-9

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large scale matroid enumeration and analysis of orientation2008

    • Author(s)
      Y. Matsumoto, S. Moriayma, H. Imai and D. Bremner
    • Journal Title

      Proceedings of the Kyoto RIMS Workshop on Computational Geometry and Discrete Mathematics Vol.1

      Pages: 10-13

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 幾何から量子そしてその先2011

    • Author(s)
      今井浩
    • Organizer
      「計算幾何学の発展と未来」研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2011-03-11
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 量子グラフ状態による情報処理2010

    • Author(s)
      今井浩,夫紀恵,森山園子
    • Organizer
      「ナノ量子情報エレクトロニクスの進展」シンポジウム
    • Place of Presentation
      東京大学
    • Year and Date
      2010-12-22
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Feynmannの2つの提唱からグラフと計算量への展開2010

    • Author(s)
      今井浩
    • Organizer
      電子情報通信学会第23回量子情報技術研究会
    • Place of Presentation
      東京大学
    • Year and Date
      2010-11-15
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] periodic graphのstatic graphに関する一考察2010

    • Author(s)
      橋倉彰宏,夫紀恵,今井浩
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      長岡技術科学大学
    • Year and Date
      2010-09-29
    • Related Report
      2010 Final Research Report
  • [Presentation] Standardization Directions of Geographic Information2009

    • Author(s)
      今井浩
    • Organizer
      Japanese- Austrian Workshop on Natural Language and Spatio-Temporal Information
    • Place of Presentation
      東京大学山上会館
    • Year and Date
      2009-09-30
    • Related Report
      2010 Final Research Report
  • [Presentation] Standardization directions of geographic information2009

    • Author(s)
      Hiroshi Imai
    • Organizer
      Japanese-Austrian Workshop on Natural Language and Spatio-Temporal Information
    • Place of Presentation
      東京大学山上会館
    • Year and Date
      2009-09-30
    • Related Report
      2009 Annual Research Report
  • [Presentation] periodic graphに関する-考察2009

    • Author(s)
      橋倉彰宏、夫紀恵、今井浩
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      長岡技術科学大学
    • Year and Date
      2009-09-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Quantum Computational Geometry and Quantum Cryptography2009

    • Author(s)
      今井浩
    • Organizer
      2009 International Workshop on Computing
    • Place of Presentation
      台湾,台北市(Keynote)
    • Year and Date
      2009-06-16
    • Related Report
      2010 Final Research Report
  • [Presentation] Quantum Computational Geometry and Quantum Cryptography2009

    • Author(s)
      Hiroshi Imai
    • Organizer
      2009 International Workshop on Computing
    • Place of Presentation
      Academia Scinica(台湾,台北市)
    • Year and Date
      2009-06-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] Guaranteeing the Security Quantitive for a Generalized Decoy State Quantum Key Protocol Incorporating Finite Statistics, Invited Talk2008

    • Author(s)
      今井浩
    • Organizer
      国際シンポジウム-量子技術に関する物理-
    • Place of Presentation
      奈良県新公会堂
    • Year and Date
      2008-11-28
    • Related Report
      2010 Final Research Report
  • [Presentation] Guaranteeing the security quantitive for a generalized decoy state quantum key protocol incorporating finite statistics (invited)2008

    • Author(s)
      H. Imai
    • Organizer
      国際シンポジウムー量子技術に関する物理-
    • Place of Presentation
      奈良県新公会堂
    • Year and Date
      2008-11-28
    • Related Report
      2008 Annual Research Report
  • [Presentation] BDDを用いたグラフのTutte多項式計算の再考察2008

    • Author(s)
      今井浩,今井桂子,松本宜丈,森山園子
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      東北大学
    • Year and Date
      2008-10-10
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation]2008

    • Author(s)
      今井浩
    • Organizer
      組合せ最適化セミナー
    • Place of Presentation
      京都大学数理解析研究所(招待講演)
    • Year and Date
      2008-07-29
    • Related Report
      2010 Final Research Report
  • [Presentation] 量子情報と組合せ・半定値最適化(invited)2008

    • Author(s)
      今井浩
    • Organizer
      組合せ最適化セミナー
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-07-29
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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