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New Developments in Computer Algebra using Techniques from Quantum Computing

Research Project

Project/Area Number 22800006
Research Category

Grant-in-Aid for Research Activity Start-up

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

Principal Investigator

LE GALL Francois  東京大学, 大学院・情報理工学系研究科, 講師 (50584299)

Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,068,000 (Direct Cost: ¥2,360,000、Indirect Cost: ¥708,000)
Fiscal Year 2011: ¥1,443,000 (Direct Cost: ¥1,110,000、Indirect Cost: ¥333,000)
Fiscal Year 2010: ¥1,625,000 (Direct Cost: ¥1,250,000、Indirect Cost: ¥375,000)
Keywordsアルゴリズム / 計算機代数 / 量子計算
Research Abstract

We developed new approaches based on techniques from quantum computing to efficiently handle computational problems with an algebraic structure. Among our main results, we constructed new algorithms for distinguishing, in the framework of property testing, classes of groups, and new quantum algorithms for computing efficiently the product of two Boolean matrices. As applications of these novel approaches, we succeeded in proving the hardness of decoding problems arising in quantum communication, and in constructing new protocols for several tasks such as privacy-preserving communication.

Report

(3 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • Research Products

    (28 results)

All 2012 2011 2010 Other

All Journal Article (10 results) (of which Peer Reviewed: 9 results,  Open Access: 1 results) Presentation (17 results) Remarks (1 results)

  • [Journal Article] Improved Output-Sensitive Quantum Algorithms for Boolean Matrix Multiplication2012

    • Author(s)
      F. Le Gall
    • Journal Title

      Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms(SODA 2012)

      Pages: 1464-1476

    • URL

      http://siam.omnibooksonline.com/2012SODA/data/papers/183.pdf

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Property Testing for Cyclic Groups and Beyond2012

    • Author(s)
      F. Le Gall, Y. Yoshida
    • Journal Title

      Journal of Combinatorial Optimization

      Volume: (印刷中) Issue: 4 Pages: 636-654

    • DOI

      10.1007/s10878-011-9445-8

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the distance between non-isomorphic groups2011

    • Author(s)
      G. Ivanyos, F. Le Gall, Y. Yoshida
    • Journal Title

      European Journal of Combinatorics

      Volume: Vol.33, No.4 Issue: 4 Pages: 474-476

    • DOI

      10.1016/j.ejc.2011.10.009

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The One-Way Communication Complexity of Subgroup Membership2011

    • Author(s)
      S. Aaronson, F. Le Gall, A. Russell, S. Tani
    • Journal Title

      Chicago Journal of Theoretical Computer Science

      Volume: 17 Issue: 1 Pages: 1-16

    • DOI

      10.4086/cjtcs.2011.006

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quantum Property Testing of Group Solvability2011

    • Author(s)
      Y. Inui, F. Le Gall
    • Journal Title

      Algorithmica

      Volume: Vol.59, No.1 Issue: 1 Pages: 35-47

    • DOI

      10.1007/s00453-009-9338-8

    • Related Report
      2011 Final Research Report
  • [Journal Article] Constructing quantum network coding schemes from classical nonlinear protocols2011

    • Author(s)
      Hirotada Kobayashi, Francois Le Gall, Harumichi Nishimura, Martin Roetteler
    • Journal Title

      Proceedings of IEEE International Symposium on Information Theory 2011

      Pages: 109-113

    • DOI

      10.1109/isit.2011.6033701

    • NAID

      110008726047

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] NP-hardness of Decoding Quantum Error Correction Codes2011

    • Author(s)
      M.-H. Hsieh, F. Le Gall
    • Journal Title

      Physical Review A

      Volume: Vol.83 Issue: 5 Pages: 52331-52331

    • DOI

      10.1103/physreva.83.052331

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quantum Property Testing of Group Solvability2011

    • Author(s)
      乾義文, ルガルフランソワ
    • Journal Title

      Algorithmica

      Volume: Vol.59 Pages: 35-47

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] NP-hardness of Decoding Quantum Error Correction Codes2011

    • Author(s)
      Min-Hsiu Hsieh, ルガルフランソワ
    • Journal Title

      Physical Review A

      Volume: 印刷中

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perfect Quantum Network Communication Protocol Based on Classical Network Coding2010

    • Author(s)
      H. Kobayashi, F. Le Gall, H. Nishimura, M. Roetteler
    • Journal Title

      Proceedings of the 2010 IEEE International Symposium on Information Theory(ISIT 2010)

      Pages: 2686-2690

    • DOI

      10.1109/isit.2010.5513644

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Presentation] 量子中継器ネットワークのための量子ネットワークコーディング2012

    • Author(s)
      佐藤貴彦,ルガルフランソワ
    • Organizer
      第25回量子情報技術研究会(QIT 25)
    • Place of Presentation
      大阪大学
    • Year and Date
      2012-01-22
    • Related Report
      2011 Final Research Report
  • [Presentation] On QMA Protocols with Two Short Quantum Proofs2012

    • Author(s)
      F. Le Gall, S. Nakagawa, H. Nishimura
    • Organizer
      第25回量子情報技術研究会(QIT 25)
    • Place of Presentation
      大阪大学
    • Year and Date
      2012-01-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Improved Output-Sensitive Quantum Algorithms for Boolean Matrix Multiplication2012

    • Author(s)
      ルガルフランソワ
    • Organizer
      23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012)
    • Place of Presentation
      Kyoto, Japan
    • Year and Date
      2012-01-19
    • Related Report
      2011 Annual Research Report
  • [Presentation] Improved Output-Sensitive Quantum Algorithms for Boolean Matrix Multiplication2011

    • Author(s)
      F. Le Gall
    • Organizer
      15th Workshop on Quantum Information Processing(QIP 2012)
    • Place of Presentation
      Montreal(カナダ)
    • Year and Date
      2011-12-15
    • Related Report
      2011 Final Research Report
  • [Presentation] Quantum Coloring Games via Symmetric SAT Games2011

    • Author(s)
      J. Fukawa, H. Imai, F. Le Gall
    • Organizer
      11th Asian Quantum Information Science Conference(AQIS 2011)
    • Place of Presentation
      Busan(韓国)
    • Year and Date
      2011-08-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Property Testing for Cyclic Groups and Beyond2011

    • Author(s)
      F. Le Gall
    • Organizer
      17th Annual International Computing and Combinatorics Conference(COCOON 2011)
    • Place of Presentation
      Dallas(アメリカ)
    • Year and Date
      2011-08-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Property Testing for Cyclic Groups and Beyond2011

    • Author(s)
      ルガルフランソワ
    • Organizer
      17th Annual International Computing and Combinatorics Conference (COCOON 2011)
    • Place of Presentation
      Dallas, USA
    • Year and Date
      2011-08-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Reconstructing Strings from Substrings with Quantum Queries2011

    • Author(s)
      R. Cleve, K. Iwama, F. Le Gall, H. Nishimura, S. Tani, J. Teruyama, S. Yamashita
    • Organizer
      4th Annual Meeting of the Asian Association for Algorithms and Computation(AAAC 2011)
    • Place of Presentation
      HsinChu(台湾)
    • Year and Date
      2011-04-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Constructing Quantum Network Coding Schemes from Classical Nonlinear Protocols2011

    • Author(s)
      H. Kobayashi, F. Le Gall, H. Nishimura, M. Roetteler
    • Organizer
      14th Workshop on Quantum Information Processing(QIP 2011)
    • Place of Presentation
      Singapore(シンガポール)
    • Year and Date
      2011-01-13
    • Related Report
      2011 Final Research Report
  • [Presentation] Constructing Quantum Network Coding Schemes from Classical Nonlinear Protocols2011

    • Author(s)
      小林弘忠, ルガルフランソワ, 西村治道, Martin Roetteler
    • Organizer
      The 14^<th> workshop on Quantum Information Processing (QIP 2011)
    • Place of Presentation
      シンガポール(シンガポール)
    • Year and Date
      2011-01-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] 量子ネットワーク符号2010

    • Author(s)
      ルガルフランソワ
    • Organizer
      第23回量子情報技術研究会(QIT 23)
    • Place of Presentation
      東京大学
    • Year and Date
      2010-11-15
    • Related Report
      2011 Final Research Report
  • [Presentation] 量子ネットワーク符号2010

    • Author(s)
      ルガルフランソワ
    • Organizer
      第23回量子情報技術研究会(QIT 23)
    • Place of Presentation
      東京大学(東京都)
    • Year and Date
      2010-11-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Quantum Algorithms for Algebraic Problems2010

    • Author(s)
      F. Le Gall
    • Organizer
      Workshop on Post-Quantum Security Models
    • Place of Presentation
      Paris(フランス)
    • Year and Date
      2010-10-12
    • Related Report
      2011 Final Research Report
  • [Presentation] Quantum Algorithms for Algebraic Problems2010

    • Author(s)
      ルガルフランソワ
    • Organizer
      Workshop on Post-Quantum Security Models
    • Place of Presentation
      パリ(フランス)
    • Year and Date
      2010-10-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] Perfect Quantum Network Communication Protocol Based on Classical Network Coding2010

    • Author(s)
      小林弘忠, ルガルフランソワ, 西村治道, Martin Roetteler
    • Organizer
      2010 1EEE International Symposium on Information Theory (ISIT 2010)
    • Place of Presentation
      オスティン(アメリカ)
    • Year and Date
      2010-06-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] An Efficient Quantum Algorithm for some Instances of the Group Isomorphism Problem2010

    • Author(s)
      F. Le Gall
    • Organizer
      第22回量子情報技術研究会(QIT 22)
    • Place of Presentation
      大阪大学
    • Year and Date
      2010-05-11
    • Related Report
      2011 Final Research Report
  • [Presentation] An Efficient Quantum Algorithm for some Instances of the Group Isomorphism Problem2010

    • Author(s)
      ルガルフランソワ
    • Organizer
      第22回量子情報技術研究会(QIT 22)
    • Place of Presentation
      大阪大学(大阪府)
    • Year and Date
      2010-05-11
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://francoislegall.com/

    • Related Report
      2011 Final Research Report

URL: 

Published: 2010-08-27   Modified: 2016-04-21  

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