Fundamental Study for Bayesian Network Systems based on Quantum-Mechanical Fluctuation

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The main purpose of the present project is to extend some probabilistic models for probabilistic inference to quantum-mechanical ones and to construct algorithms for the corresponding belief propagation method. The fundamental studies of the quantum-mechanical belief propagation is based on the advanced mean field methods, particularly, the cluster variation method. The conventional belief propagation cannot be applied to the quantized probabilistic models. In the present project, the new belief propagation algorithm has been derived for quantum-mechanical extended probabilistic inference systems. And the general formula for quantum-mechanical belief propagation method has been given. The algorithm usually includes an iterative procedure. The convergence of the iterative procedure is important for applications of the intelligent information processing systems.Some results have been opened in some invited talks of the following Workshop and Symposiums:1. Workshop on Mathematics of Statistical Inference (December, 2005, Tokyo Institute of Technology)2. Symposium of the MEXT Grant-in-Aid for Scientific Research on Priority Areas "Deepening and Expansion of Statistical Mechanical Informatics" (December 2006, Tokyo)3. Symposium of the 2007 Spring Meeting in the Physical Society of Japan, "Statistical Mechanical Informatics for Quantum Systems" (March 2007, Kagoshima University)