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

2010 Fiscal Year Final Research Report

• Project/Area Number: 20300002
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: The 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
• 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

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.

Research Products

• [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
  • 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
  • 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
  • Peer Reviewed
• [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
  • 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
  • Peer Reviewed
• [Journal Article] Computational Geometry Analysis of Quantum State Space and Its Applications (2008)
  • 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
• [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
  • 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
  • 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
  • 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
  • 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
  • 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
• [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
• [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
• [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
• [Presentation] Standardization Directions of Geographic Information (2009)
  • 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
• [Presentation] Quantum Computational Geometry and Quantum Cryptography (2009)
  • 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
• [Presentation] Guaranteeing the Security Quantitive for a Generalized Decoy State Quantum Key Protocol Incorporating Finite Statistics, Invited Talk (2008)
  • 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
• [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
• [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