Rapid quantum state transfer based on bang-bang Lyapunov control under various dissipative modes

In quantum state transfer and tracking, fast control of quantum states are effective against the decoherence caused by external environment and information processing. The variational method and maximum principle are often used to solve the time-optimal control problems. However, analytic results cannot be obtained for many cases and it is necessary to find methods that can solve optimal control problems very efficiently. By comparing the advantages and disadvantages of the existing Lyapunov control and bang-bang control, we apply in this paper a new method that combines bang-bang control and Lyapunov control and can solve the time-optimal control problems in the open quantum system. Numerical simulations for a two-level open quantum system validate the effectiveness of the method. Furthermore, the optimized scheme avoids high frequency oscillation that occurs in bang-bang control.