Switching control of closed quantum systems via the Lyapunov method

In this paper, we consider the state transfer problem for closed quantum systems under a degenerate case, where the linearized system around the target state is not controllable. It is known that the traditional Lyapunov control methods may fail to guarantee the convergence to the target state under the degenerate case. Hence, we propose to use multiple Lyapunov functions and design a switching control strategy to achieve more accurate state transfer. It is shown that the system can converge to the intersection of invariant sets including the target state. The explicit analysis of the convergence is provided to design the switching law. Moreover, the effectiveness of open-loop Lyapunov control is discussed. Simulation studies are presented to show the improved control performance.