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

研究了量子力学横向场中无限范围Ising自旋玻璃描述的纠错码。我们利用复制方法评估了贝叶斯最优解的统计性能，并讨论了香农界与铁磁体- spingglass相变发生临界点的关系。我们还构建了TAP方程的量子力学变体，以实现香农界附近的性能。接下来，我们根据量子蒙特卡罗方法提出了描述系统演化动力学过程的理论框架，并从微观主方程推导出关于磁化等宏观量的微分方程。我们澄清了静态近似在一些有限情况下的有效性。在量子退火的简并、量子反铁磁体的相变和所谓的数字半调的自旋波理论分析方面，我们也获得了一些研究成果。

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.