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Population control of quantum states based on invariant subsets under a diagonal Lyapunov function

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3 Author(s)
Sen Kuang ; Dept. of Autom., Univ. of Sci. & Technol. of China, Hefei, China ; Shuang Cong ; Yuesheng Lou

This paper deduces and analyzes the invariant set in quantum Lyapunov control, explores the principles for constructing and adjusting diagonal elements of a diagonal Lyapunov function, and achieves the convergence to any goal state in some invariant subset of closed loop systems by using dynamical system theory and energy-level connectivity graph. Research results show that if a goal state is an eigenstate of the inner Hamiltonian, then it is very easy to achieve convergence to the goal state with a high probability; and if a goal state is a superposition state in some invariant subset, then it is possible to achieve satisfactory control when the diagonal elements are properly constructed.

Published in:

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Date of Conference:

15-18 Dec. 2009