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Exploiting Matroid Minor Theory and Its Connection with Quantum Computing Models

Research Project

Project/Area Number 26540004
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Theory of informatics
Research InstitutionThe University of Tokyo

Principal Investigator

IMAI Hiroshi  東京大学, 大学院情報理工学系研究科, 教授 (80183010)

Co-Investigator(Renkei-kenkyūsha) MORIYAMA Sonoko  日本大学, 文理学部, 教授 (20361537)
Research Collaborator HIRAISHI Hidefumi  東京大学, 大学院情報理工学系研究科, 助教 (70795335)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywordsアルゴリズム理論 / 有向マトロイド / 量子コンピュータ / 量子計算 / 量子ネットワーク符号化 / 拡張複雑度
Outline of Final Research Achievements

This research investigated computation power of quantum computing, specifically measurement-based quantum computing, in terms of parameters developed in matroid minor theory by extending the theory itself. The power is characterized by the widths of matroids, and then a new approach using the BDD representing a quantum state is developed. The database of matroids of moderate sizes has been also maintained to use it for future computational analysis.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (26 results)

All 2016 2015 2014

All Journal Article (9 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 9 results,  Open Access: 2 results) Presentation (17 results) (of which Int'l Joint Research: 4 results,  Invited: 5 results)

  • [Journal Article] A Lower Bound on Opaque Sets2016

    • Author(s)
      Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, Janos Pach
    • Journal Title

      Proc. of the 32nd Symposium on Computational Geometry

      Volume: 32

    • DOI

      10.4230/LIPIcs.SoCG.2016.46

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Parametric multiroute flow and its application to multilink-attack network2016

    • Author(s)
      Jean-Francois Baffier, Vorapong Suppakitpaisarn, Hidefumi Hiraishi and Hiroshi Imai
    • Journal Title

      Discrete Optimization

      Volume: 22 Pages: 20-36

    • DOI

      10.1016/j.disopt.2016.05.002

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semimetric Properties of Sorensen-Dice and Tversky Indexes2016

    • Author(s)
      Alonso Gragera, Vorapong Suppakitpaisarn
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9627 Pages: 339-350

    • DOI

      10.1007/978-3-319-30139-6_27

    • ISBN
      9783319301389, 9783319301396
    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Parameterized Algorithms to Compute Ising Partition Function2015

    • Author(s)
      Hidefumi Hiraishi, Hiroshi Imai, Yoichi Iwata, Bingkai Lin
    • Journal Title

      Proceedings of the 9th Hungarian-Japanese Symposium on Discrete Mathematics and Its Application

      Volume: 1 Pages: 212-220

    • NAID

      130007479457

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Minimal non-roientable matroids of rank three.2015

    • Author(s)
      Hidefumi Hiraishi and Sonoko Moriyama
    • Journal Title

      European Journal of Combinatorics (in press)

      Volume: - Pages: 123-137

    • DOI

      10.1016/j.ejc.2015.03.025

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Extended Complexity of Lower-Truncated Transversal Polymatroids2015

    • Author(s)
      Shuichi Hirahara, Hidefumi Hiraishi, Hiroshi Imai
    • Journal Title

      The 18th Korea-Japan Joint Workshop on Algorithms and Computation (WAAC2015)

      Volume: 1 Pages: 17-20

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Parameterized Algorithms to Compute Ising Partition Function.2015

    • Author(s)
      Hidefumi Hiraishi, Hiroshi Imai, Yoichi Iwata, Bingkai Lin
    • Journal Title

      Proceedings of the 9th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications, to appear.

      Volume: -

    • NAID

      130007479457

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Orientable or Representable Matroids over Infinite Fields of Rank 32015

    • Author(s)
      Hidefumi Hiraishi, Sonoko Moriyama
    • Journal Title

      Proceedings of the 9th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications, to appear.

      Volume: -

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] BDD Operations for Quantum Graph States.2014

    • Author(s)
      H. Hiraishi and H. Imai
    • Journal Title

      Proc. 6th Int. Conf. on Reversible Computation, LNCS

      Volume: 8507 Pages: 216-229

    • DOI

      10.1007/978-3-319-08494-7_17

    • ISBN
      9783319084930, 9783319084947
    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] A Note on Extended Formulations of Lower-truncated Transversal Polymatroids2016

    • Author(s)
      Hidefumi Hiraishi, Shuichi Hirahara, Hiroshi Imai
    • Organizer
      The fifth International Conference on Continuous Optimization
    • Place of Presentation
      政策研究大学院大学, 東京都
    • Year and Date
      2016-08-11
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Geometric Optimization Related with an LCP with SPD-matrices2016

    • Author(s)
      Sonoko Moriyama, Bernd Gaertner, Hiroshi Imai, Hiroyuki Miyazawa, Jiro Nishitoba
    • Organizer
      The fifth International Conference on Continuous Optimization
    • Place of Presentation
      政策研究大学院大学, 東京都
    • Year and Date
      2016-08-11
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 媒介中心性に基づくシャプレイ値の高速近似計算アルゴリズム2016

    • Author(s)
      上里晃平, 大坂直人, 平石秀史
    • Organizer
      夏のLAシンポジウム
    • Place of Presentation
      かんぽの宿・大和平群, 奈良県
    • Year and Date
      2016-07-20
    • Related Report
      2016 Annual Research Report
  • [Presentation] Q[x]-representable Excluded Minors for Q-Representable Matroids of Rank Three2016

    • Author(s)
      Sonoko Moriyama, Hidefumi Hiraishi
    • Organizer
      2016 International Workshop on Structure in Graphs and Matroids
    • Place of Presentation
      Eindhoven, Netherlands
    • Year and Date
      2016-07-15
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Excluded Minors for Matroids of Rank Three2016

    • Author(s)
      Sonoko Moriyama, Hidefumi Hiraishi
    • Organizer
      SIAM on Conference on Discrete Mathematics
    • Place of Presentation
      Atlanta, USA
    • Year and Date
      2016-06-06
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Parameterized algorithms to compute Ising partition function via graph decompositions2016

    • Author(s)
      Hiroshi Imai
    • Organizer
      The 75th Okazaki Conference Tensor Network States: Algorithms and Applications 2016
    • Place of Presentation
      岡崎コンファレンスセンター, 愛知県岡崎市
    • Year and Date
      2016-01-11
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Tree Tensor Network, Quantum Computing, and Graph Minor Theory2016

    • Author(s)
      Hidefumi Hiraishi
    • Organizer
      The 75th Okazaki Conference Tensor Network States: Algorithms and Applications 2016
    • Place of Presentation
      岡崎コンファレンスセンター, 愛知県岡崎市
    • Year and Date
      2016-01-11
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Excluded Minors for$\mathbb{Q}$-Representable Matroids in Algebraic Extension2015

    • Author(s)
      Hidefumi Hiraishi and Sonoko Moriyama
    • Organizer
      The 18th Japan Conference on Discrete and Computationa
    • Place of Presentation
      京都大学, 京都府京都市
    • Year and Date
      2015-09-14
    • Related Report
      2015 Research-status Report
  • [Presentation] Benchmark test on solution quality for max cut solvers2015

    • Author(s)
      Hiroshi Imai, Yosuke Yano, Satoru Yasuda
    • Organizer
      The 15th Asian Quantum Information Science Conference (AQIS)
    • Place of Presentation
      ソウル, 韓国
    • Year and Date
      2015-08-24
    • Related Report
      2015 Research-status Report
  • [Presentation] Efficient Parameterized Algorithm to Compute Planar Ising Partition Function2015

    • Author(s)
      Hidefumi Hiraishi, Hiroshi Imai, Yoichi Iwata, Bingkai Lin
    • Organizer
      The 15th Asian Quantum Information Science Conference (AQIS)
    • Place of Presentation
      ソウル, 韓国
    • Year and Date
      2015-08-24
    • Related Report
      2015 Research-status Report
  • [Presentation] Benchmark test on solution quality for max cut solvers2015

    • Author(s)
      安田智, 矢野洋祐, 今井浩
    • Organizer
      夏のLAシンポジウム
    • Place of Presentation
      ゆのくに天祥, 石川県加賀市
    • Year and Date
      2015-07-14
    • Related Report
      2015 Research-status Report
  • [Presentation] グラフの最大カット問題と汎用最適化ソフトウェア2015

    • Author(s)
      今井浩, 矢野洋祐
    • Organizer
      量子情報技術研究会(QIT32)
    • Place of Presentation
      大阪大学, 大阪府豊中市
    • Year and Date
      2015-05-25
    • Related Report
      2015 Research-status Report
  • [Presentation] Extended Formulations of Cut Polytopes and Quantum Correlation/Interaction.2014

    • Author(s)
      H. Imai, H. Hiraishi, and S. Hirahara
    • Organizer
      第31回量子情報技術研究会 (QIT 31)
    • Place of Presentation
      東北大学, 宮城県
    • Year and Date
      2014-11-18
    • Related Report
      2014 Research-status Report
  • [Presentation] On Extended Complexity of Generalized Transversal Matroids.2014

    • Author(s)
      S. Hirahara and H. Imai
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      中央大学, 東京都
    • Year and Date
      2014-10-08
    • Related Report
      2014 Research-status Report
  • [Presentation] BDD Representations for Quantum Graph State and Ising Model.2014

    • Author(s)
      H. Hiraishi, H. Imai, Y. Iwata and B. Lin
    • Organizer
      Asian Quantum Information Science Conference 2014 (AQIS 2014)
    • Place of Presentation
      芝蘭会館, 京都府
    • Year and Date
      2014-08-20
    • Related Report
      2014 Research-status Report
  • [Presentation] Minimal non-orientable matroids of rank three.2014

    • Author(s)
      Sonoko Moriyama
    • Organizer
      2014 International Workshop on Structure in Graphs and Structures
    • Place of Presentation
      プリンストン大学, アメリカ合衆国
    • Year and Date
      2014-07-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Excluded minors for orientability and representability of matroids.2014

    • Author(s)
      Hidefumi Hiraishi
    • Organizer
      2014 International Workshop on Structure in Graphs and Matroids
    • Place of Presentation
      プリンストン大学, アメリカ合衆国
    • Year and Date
      2014-07-21
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2018-03-22  

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