State preservation and characteristic analysis for open quantum system control

In the case of fixed system frequency and ambient temperature, we design a Lyapunov-based controller to transfer and maintain states for the Time-convolution-less (TCL) master equation of two-level non-Markovian open quantum systems. Basis on the state transferring from the superposition state to superposition state, we maintain the state in the superposition state. The system simulation experiments are implemented under the MATLAB environment. The comparison experiments of the fault-tolerant performance before and after maintaining state demonstrate the superiority of the designed controller. At the same time, the influence of control parameters to length of time maintaining the state of the system are analyzed, and the best control parameters are given.