Population Control of Equilibrium States of Quantum Systems via Lyapunov Method
Sen Kuang, Shuang Cong · Acta Automatica Sinica · 2010
摘要: This paper studies the population control problem associated with the equilibrium states of mixed-state quantum systems by using a Lyapunov function with degrees of freedom. The control laws are designed by ensuring the monotonicity of the Lyapunov function; main results on the largest invariant set in the sense of LaSalle are given; and the strict expression of any state in the largest invariant set is normally deduced in the framework of Bloch vectors. By analyzing the obtained largest invariant set and the Lyapunov function itself, this paper also discusses the determination problem of the degrees of freedom. Numerical simulation experiments on a three-level system show the validity of research results. 关键词: Quantum system / population control / Bloch vector / Lyapunov function / invariant set