Control Methods of Closed Quantum Systems

Abstract

Optimal control is a very important strategy in control theory, and in recent years optimal control theory for quantum systems has received considerable attention (Rice and Zhao, 2000;Khaneja, Brockett, and Glaser, 2001;D'Alessandro, 2002). The key concept of optimal control is that the control law will be obtained by means of minimizing a cost function. As a result, choosing an appropriate cost function is one of the central tasks in the process of optimal control. Unlike the optimal control in macroscopic systems, the choice of the cost function in microcosmic systems must be considered according to the properties of quantum systems. Upon to now, the cost functions of quantum systems have mainly been of the following types:Control of Quantum Systems: Theory and Methods, First Edition. Shuang Cong. Control of Quantum Systems3. Select the optimal unitary transformation as the cost function Kosloff, 2002, 2003). In such a case, the system dynamics are fully specified by the evolution operator U(t), and the desired unitary operator is U d . One must endeavor to control the quantum system to satisfy the equation U(T) = e i U d . Thus the cost function is: