An improved differential evolution algorithm for learning high-fidelity quantum controls

Precisely and efficiently designing control pulses for the preparation of quantum states and quantum gates are the fundamental tasks for quantum computation. Gradient-based optimal control methods are the routine to design such pulses. However, the gradient information is often difficult to calculate or measure, especially when the system is not well calibrated or in the presence of various uncertainties. Gradient-free evolutionary algorithm is an alternative choice to accomplish this task but usually with low-efficiency. Here, we design an efficient mutation rule by using the information of the current and the former individuals together. This leads to our improved differential evolution algorithm, called daDE. To demonstrate its performance, we numerically benchmark the pulse optimization for quantum states and quantum gates preparations on small-scale NMR system. Further numerical comparisons with conventional differential evolution algorithms show that daDE has great advantages on the convergence speed and robustness to several uncertainties including pulse imperfections and measurement errors.