ANALYSIS OF QUANTUM MONTE CARLO DYNAMICS IN INFINITE-RANGE ISING SPIN SYSTEMS: THEORY AND ITS POSSIBLE APPLICATIONS

摘要

In terms of the stochastic process of a quantum-mechanical variant of Markov chain Monte Carlo method based on the Suzuki-Trotter decomposition, we analytically derive deterministic flows of order parameters such as magnetization in infinite-range (a mean-field like) quantum spin systems. Under the static approximation, differential equations with respect to order parameters are explicitly obtained from the Master equation that describes the microscopic-law in the corresponding classical system. We discuss several possible applications of our approach to several research topics, say, image processing and neural networks. This paper is written as a self-review of two papers~(1,2) for Symposium on Interface between Quantum Information and Statistical Physics at Kinki University in Osaka, Japan.