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Analysis of possibility of efficient quantum algorithms for Hidden Subgroup Problem

Research Project

Project/Area Number 20700017
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Fundamental theory of informatics
Research InstitutionNational Institute of Advanced Industrial Science and Technology

Principal Investigator

NUIDA Koji  独立行政法人産業技術総合研究所, 情報セキュリティ研究センター, 研究員 (20435762)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords応用数学 / 量子情報理論 / 状態識別問題
Research Abstract

In this research, I studied the fundamentals of quantum computers which are based on quantum physics and are expected as a candidate of powerful new-generation computers, especially from the viewpoint of quantum algorithms specialized to the quantum computers. First, I focused on quantum information theory that is a base of quantum computation, and obtained some research results on quantum state discrimination problems and on characterizations of quantum bits from physical principles. On the other hand, I investigated Hidden Subgroup Problems(HSPs) which are one of the main research topics in the area of quantum algorithms ; I revisited the known approaches to HSPs and analyzed drawbacks of these approaches, which will be future research subjects.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (30 results)

All 2011 2010 2009 Other

All Journal Article (16 results) (of which Peer Reviewed: 5 results) Presentation (12 results) Remarks (2 results)

  • [Journal Article] 量子力学の物理原理的特徴付けと凸集合の幾何学2011

    • Author(s)
      縫田光司
    • Journal Title

      北海道大学数学講究録

      Volume: 148号 Pages: 59-66

    • URL

      http://eprints3.math.sci.hokudai.ac.jp/2140/

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Journal Article] 量子力学の物理原理的特徴付けと凸集合の幾何学2011

    • Author(s)
      縫田光司
    • Journal Title

      北海道大学数学講究録 148号

      Pages: 59-66

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 物理原理に基づく量子ビット系の導出2010

    • Author(s)
      木村元,縫田光司,今井秀樹
    • Journal Title

      第33回情報理論とその応用シンポジウム(SITA2010)予稿集

      Volume: (CD-ROM)

    • Related Report
      2011 Final Research Report
  • [Journal Article] Distinguishability measures and entropies for general probabilistic theories2010

    • Author(s)
      Gen Kimura, Koji Nuida, Hideki Imai
    • Journal Title

      Reports on Mathematical Physics

      Volume: vol.66 Issue: 2 Pages: 175-206

    • DOI

      10.1016/s0034-4877(10)00025-x

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal observables for minimum-error state discrimination in general probabilistic theories2010

    • Author(s)
      Koji Nuida, Gen Kimura, Takayuki Miyadera
    • Journal Title

      Journal of Mathematical Physics

      Volume: vol.51 Issue: 9 Pages: 93505-93505

    • DOI

      10.1063/1.3479008

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Distinguishability measures and entropies for general probabilistic theories2010

    • Author(s)
      Gen Kimura, Koji Nuida, Hideki Imai
    • Journal Title

      Reports on Mathematical Physics vol.66

      Pages: 175-206

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Optimal observables for minimum-error state discrimination in general probabilistic theories2010

    • Author(s)
      Koji Nuida, Gen Kimura, Takayuki Miyadera
    • Journal Title

      Journal of Mathematical Physics vol.51

      Pages: 93505-93505

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids2010

    • Author(s)
      Gen Kimura, Koji Nuida
    • Journal Title

      e-Print arXiv

      Volume: 1012.5350

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Physical equivalence of pure states and derivation of qubit in general probabilistic theories2010

    • Author(s)
      Gen Kimura, Koji Nuida, Hideki Imai
    • Journal Title

      e-Print arXiv

      Volume: 1012.5361

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 量子計算、量子アルゴリズムと有限群の表現論2009

    • Author(s)
      縫田光司
    • Journal Title

      2009年度表現論シンポジウム講演集

      Pages: 74-85

    • NAID

      130008004896

    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report 2009 Annual Research Report
  • [Journal Article] 一般確率モデルから眺める量子情報理論2009

    • Author(s)
      縫田光司
    • Journal Title

      北海道大学数学講究録

      Volume: 140号 Pages: 37-41

    • URL

      http://eprints3.math.sci.hokudai.ac.jp/1980/

    • Related Report
      2011 Final Research Report
  • [Journal Article] On two-state discrimination problems in generic probability models2009

    • Author(s)
      縫田光司,木村元,宮寺隆之
    • Journal Title

      2009年暗号と情報セキュリティシンポジウム(SCIS2009)予稿集

      Volume: (CD-ROM)

    • Related Report
      2011 Final Research Report
  • [Journal Article] 一般確率モデルから眺める量子情報理論2009

    • Author(s)
      縫田光司
    • Journal Title

      北海道大学数学講究録 140号

      Pages: 37-41

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Optimal Observables for Minimum-Error State Discrimination in General Probabilistic Theories2009

    • Author(s)
      Koji Nuida, Gen Kimura, Takayuki Miyadera
    • Journal Title

      e-Print arXiv 0906.5419

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Distinguishability Measures and Entropies for General Probabilistic Theories2009

    • Author(s)
      Gen Kimura, Koji Nuida, Hideki Imai
    • Journal Title

      e-Print arXiv 0910.0994

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 一般確率モデルから眺める量子情報理論2009

    • Author(s)
      縫田光司
    • Journal Title

      北海道大学数学講究録 140

      Pages: 37-41

    • Related Report
      2008 Annual Research Report
  • [Presentation] 量子力学の物理原理的特徴付けと凸集合の幾何学2011

    • Author(s)
      縫田光司
    • Organizer
      第7回数学総合若手研究集会
    • Place of Presentation
      北海道大学(札幌市)
    • Year and Date
      2011-03-03
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] 量子力学の物理原理的特徴付けを凸集合の幾何学2011

    • Author(s)
      縫田光司
    • Organizer
      第7回数学総合若手研究集会
    • Place of Presentation
      北海道大学(札幌市)
    • Year and Date
      2011-03-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] On derivation of qubit systems from physical principles2011

    • Author(s)
      Koji Nuida
    • Organizer
      14th Workshop on Quantum Information Processing
    • Place of Presentation
      The Capella(Sentosa, Singapore)
    • Year and Date
      2011-01-10
    • Related Report
      2011 Final Research Report
  • [Presentation] On derivation of qubit systems from physical principles2011

    • Author(s)
      Koji Nuida
    • Organizer
      14th Workshop on Quantum Information Processing
    • Place of Presentation
      The Capella(Sentosa,Singapore)
    • Year and Date
      2011-01-10
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On derivation of qubit systems from physical principles2011

    • Author(s)
      Koji Nuida, Gen Kimura, Hideki Imai
    • Organizer
      14th Workshop on Quantum Information Processing
    • Place of Presentation
      The Capella, Sentosa, Singapore
    • Year and Date
      2011-01-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] 量子計算、量子アルゴリズムと有限群の表現論2009

    • Author(s)
      縫田光司
    • Organizer
      2009年度表現論シンポジウム
    • Place of Presentation
      フェストーネ(沖縄県)
    • Year and Date
      2009-11-18
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report 2009 Annual Research Report
  • [Presentation] 一般確率モデルから眺める量子情報理論2009

    • Author(s)
      縫田光司
    • Organizer
      第5回数学総合若手研究集会(MCYR5)
    • Place of Presentation
      北海道大学学術交流会館
    • Year and Date
      2009-03-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] On Two-State Discrimination Problems in Generic Probability Models2009

    • Author(s)
      縫田光司
    • Organizer
      2009年暗号と情報セキュリティシンポジウム(SCIS2009)
    • Place of Presentation
      大津プリンスホテル(滋賀県)
    • Year and Date
      2009-01-20
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] On Two-State Discrimination Problems in Generic Probability Models2009

    • Author(s)
      縫田光司
    • Organizer
      2009年暗号と情報セキュリティシンポジウム(SCIS2009)
    • Place of Presentation
      大津プリンスホテル
    • Year and Date
      2009-01-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] On Minimum-Error State Discrimination Problems in Generic Probability Models2009

    • Author(s)
      Koji Nuida
    • Organizer
      The Twelfth Workshop on Quantum Information Processing(QIP 2009)
    • Place of Presentation
      Santa Fe Convention Center(NM, USA)
    • Year and Date
      2009-01-14
    • Related Report
      2011 Final Research Report
  • [Presentation] On Minimum-Error State Discrimination Problems in Generic Probability Models2009

    • Author(s)
      Koji Nuida
    • Organizer
      The Twelfth Workshop on Quantum Information Processing(QIP 2009)
    • Place of Presentation
      Santa Fe Convention Center(NM,USA)
    • Year and Date
      2009-01-14
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On Minimum-Error State Discrimination Problems in Generic Probability Models2009

    • Author(s)
      Koji Nuida
    • Organizer
      The Twelfth Workshop on Quantum Information Processing (QIP 2009)
    • Place of Presentation
      Santa Fe Convention Center, NM, USA
    • Year and Date
      2009-01-14
    • Related Report
      2008 Annual Research Report
  • [Remarks] (1)(プレプリント) Gen Kimura, Koji Nuida," On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids", e-print arXiv : 1012.5350

    • URL

      http://jp.arxiv.org/abs/1012.5350

    • Related Report
      2011 Final Research Report
  • [Remarks] (2)(プレプリント) Gen Kimura, Koji Nuida, Hideki Imai," Physical equivalence of pure states and derivation of qubit in general probabilistic theories", e-print arXiv : 1012.5361

    • URL

      http://jp.arxiv.org/abs/1012.5361

    • Related Report
      2011 Final Research Report

URL: 

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

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