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2009 Fiscal Year Final Research Report

Probabilistic information processing and statistical mechanics of information by optimal controlling of quantum fluctuation

Research Project

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Project/Area Number 18079001
Research Category

Grant-in-Aid for Scientific Research on Priority Areas

Allocation TypeSingle-year Grants
Review Section Science and Engineering
Research InstitutionHokkaido University

Principal Investigator

INOUE Jun-ichi  Hokkaido University, 大学院・情報科学研究科, 准教授 (30311658)

Co-Investigator(Kenkyū-buntansha) SAIKA Yohei  和歌山工業高等専門学校, 電気情報工学科, 准教授 (40280432)
Project Period (FY) 2006 – 2009
Keywords量子統計力学 / 量子情報 / 量子揺らぎ / 情報統計力学 / スピングラス
Research Abstract

We investigated error-correcting codes described by infinite range Ising spin glasses in a quantum-mechanical transverse field. We evaluated the statistical performance for the Bayes-optimal solution by making use of the replica method and discussed the relationship between the Shannon's bound and the critical point at which the Ferromagnet-SpinGlass phase transition takes place. We also constructed a quantum-mechanical variant of the TAP equation to achieve the performance near the Shannon's bound. We next proposed a theoretical framework to describe the dynamical process of the system evolving according to the quantum Monte Carlo method and derived the differential equations with respect to the macroscopic quantities such as a magnetization from the microscopic master equation. We clarified the validity of the static approximation for some limited cases. We also obtained several results in the topic of spin wave theoretical analysis of quantum annealing with degeneracy, phase transition in the quantum anti-ferromagnets and the so-called digital halftoning by collaborating researchers in and out of our research project.

  • Research Products

    (10 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (5 results) Presentation (3 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method2010

    • Author(s)
      J. Inoue
    • Journal Title

      Journal of Physics: Conference Series (Proceedings of IW-SMI2010) (出版予定)

  • [Journal Article] Quantum phase transition in a disordered long-range transverse Ising antiferromagnet2010

    • Author(s)
      A.K. Chandra, J. Inoue, B.K. Chakrabarti
    • Journal Title

      Physical Review E Vol.81

      Pages: 02110

  • [Journal Article] Bayes-optimal inverse halftoning and statistical mechanics of the Q-Ising model2009

    • Author(s)
      Y. Saika, J. Inoue, H. Tanaka, M. Okada
    • Journal Title

      Central European Journal of Physics Vol.7

      Pages: 444-456

  • [Journal Article] Quantum mean-field decoding algorithm for error-correcting codes2009

    • Author(s)
      J. Inoue, Y. Saika, M. Okada
    • Journal Title

      Journal of Physics: Conference Series Vol.143

      Pages: 012019-1-012019-10

  • [Journal Article] Analysis of a long-range random field quantum antiferromagnetic Ising model2006

    • Author(s)
      B.K. Chakrabarti, A. Das, J. Inoue
    • Journal Title

      European Physical Journal B: Condensed Matter Physics vol.51

      Pages: 321-329

  • [Presentation] Condensation phenomena and wealth re-distribution: Statistical-mechanical analysis of disordered urn models2009

    • Author(s)
      J. Inoue, J. Ohkubo
    • Organizer
      Econophysics-Kolkata IV: International Workshop on Econophysics of Games and Social Choices
    • Place of Presentation
      Indian Statistical Institute, Kolkata, India
    • Year and Date
      2009-03-12
  • [Presentation] On the convergence of quantum-mechanical variant of the Thouless-Anderson-Palmer equation2009

    • Author(s)
      J. Inoue, Y. Saika, M. Okada
    • Organizer
      International Workshop on Quantum Phase Transition and Dynamics: Quenching, Annealing and Quantum Computation
    • Place of Presentation
      Saha Institute of Nuclear Physics, Kolkata, India
    • Year and Date
      2009-02-06
  • [Presentation] Queueing Theoretical Analysis of First Passage Processes in Foreign Currency Exchange Rate2007

    • Author(s)
      J. Inoue, N. Sazuka
    • Organizer
      Research Workshop of the Israel Science Foundation Statistical Physics and Its Applications to Complex Problems in Communication
    • Place of Presentation
      Eilat, Princess Hotel, Israel
    • Year and Date
      2007-03-14
  • [Book] ビギナーズガイド情報理論2008

    • Author(s)
      井上純一
    • Total Pages
      167
    • Publisher
      プレアデス出版
  • [Remarks]

    • URL

      http://chaosweb.complex.eng.hokudai.ac.jp/~j_inoue/

URL: 

Published: 2011-06-18   Modified: 2016-04-21  

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