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

量子涨落最优控制的概率信息处理和信息统计力学

• 批准号: 18079001
• 负责人: INOUE Jun-ichi
• 金额: $ 22.08万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18079001/
• 关键词: 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; 統計力学; 確率的情報処理; 量子モンテカルロ法; レプリカ法; 量子スピン系

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.

我们研究了量子力学横向场中无限程伊辛自旋玻璃所描述的纠错码。利用复型方法对贝叶斯最优解的统计性能进行了评估，并讨论了Shannon界与铁磁-自旋玻璃相变临界点之间的关系.我们还构造了TAP方程的量子力学变体，以实现香农限附近的性能。接下来，我们提出了一个理论框架来描述根据量子蒙特卡罗方法演化的系统的动力学过程，并从微观主方程推导出关于宏观量（如磁化强度）的微分方程。我们澄清了静态近似的有效性，为一些有限的情况下。我们还获得了一些结果的自旋波理论分析的量子退火与简并，在量子反铁磁体的相变和所谓的数字半色调的主题，通过合作的研究人员和我们的研究项目。

项目成果

群知能シミュレーションにおける異方性の創発とその解析評価

群体智能模拟中各向异性的出现及其分析评价

• 发表时间: 2009
• 作者: 巻口誉宗;井上純一
• 通讯作者: 井上純一

非一様な壺模型におけるボース凝縮と占有分布の冪則

非均匀锅模型中 Bose 凝聚的幂律和占用分布

• 发表时间: 2007
• 作者: 井上純一;大久保潤
• 通讯作者: 大久保潤

Power-law behavior and condensation phenomena in disordered urn Models: Analysis and its application to macro-economics

无序瓮模型中的幂律行为和凝聚现象：分析及其在宏观经济学中的应用

• 发表时间: 2008
• 作者: J. Inoue;J. Ohkubo
• 通讯作者: J. Ohkubo

Statistical-Mechanical Analysis of Inverse Digital-Halftoning

逆数字半色调的统计机械分析

• 发表时间: 2007
• 期刊: Proceedings of the 7th International Conference on Intelligent Systems Design and Applications (ISDA'07) 1
• 作者: J. Inoue;Y. Saika;M. Okada
• 通讯作者: M. Okada

On the convergence of quantum-mechanical variant of the Thouless-Anderson-Palmer equation International Workshop on Quantum Phase Transition and Dynamics: Quenching Annealing and Quantum Computation

关于 Thouless-Anderson-Palmer 方程的量子力学变体的收敛性 量子相变和动力学国际研讨会：淬火退火和量子计算

• 发表时间: 2009
• 作者: J. Inoue;Y. Saika and M. Okada
• 通讯作者: Y. Saika and M. Okada