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Quantum Mechanical Theory of Nonlinear Optimal Control

哲郎 伊丹

Published Jan 23, 2004• 0 citations
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In this paper, the relations between theories of the quantum mechanics and the stochastic control are briefly surveyed based on the recent works of the author (Ohsumi, $1989a(Ohsumi, $ ,$ $1989b(Ohsumi, $ $ , 1992)).Concretely, two types of (nonlinear) Schr\"odinger eqations from the stochsatic control theory by introducing wavefunctions which connect two solutions of nonlinear filtering equation and stochastic optimal control problem.Furthermore, an inverse prob- lem is investigated to derive the optimal control problem from a given Schr\"odinger equation.
We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in quantum optimal control theory (QOCT). We show how the nonlinear equations of QOCT can be viewed as a "fixed-point" nonlinear problem. The iterative algorithms for this class of problems may benefit from mixing strategies, as it happens, e.g., in the quest for the ground-state density in Kohn-Sham density-functional theory. We demonstrate, with some numerical examples, how the same mixing schemes utilized in this latter nonlinear problem may significantly accelerate the QOCT iterative procedures.