Learning Control with Evolution Strategy for Inhomogeneous Open Quantum Ensembles

This paper investigates the application of an evolutionary algorithm, evolution strategy (ES)($\mu+\lambda$) to the control design in several inhomogeneous open quantum ensembles. We apply the ES ($\mu+\lambda$) to assist the sampling-based learning control (SLC) technique, by which a set of control signals is designed to drive the inhomogeneous open quantum ensemble to a given target state. We illustrate our algorithm in two-level and four-level inhomogeneous open quantum ensembles. Numerical results show the effectiveness of the proposed control algorithm. The comparison with other evolutionary algorithms such as differential evolution (DE) and genetic algorithm (GA) shows the superiority of our ES ($\mu+\lambda$) both in average fidelity and stability. In a four-level open quantum ensemble, for example, the fitness error after optimization using the ES ($\mu+\lambda$) is decreased by around 59% compared to DE, and the standard deviation is lowered by about 47%.