2009 Fiscal Year Final Research Report
Probabilistic information processing and statistical mechanics of information by optimal controlling of quantum fluctuation
| Project/Area Number |
18079001
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Hokkaido University |
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Principal Investigator |
INOUE Jun-ichi Hokkaido University, 大学院・情報科学研究科, 准教授 (30311658)
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| 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)
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| Project Period (FY) |
2006 – 2009
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| 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 |
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| 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.
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