Lyapunov-based control for the operator preparation in Markovian open quantum systems

We design the control laws which can be used to prepare operators based on quantum Lyapunov control method for two level Markovian open quantum systems in this paper. For the operator preparation, an often used Lyapunov function is the distance V_dis between the evolution operator U (t) and the target operator U_f. We construct a novel Lyapunov function V which is from the matrix logarithm function log U^†_fU (t). The convergence speeds and numerical values of V and V_dis are analyzed in detail. The control laws which are used to prepare operators are designed based on the proposed V. Numerical experiments are carried out to verify the superiority of the designed control laws.