Learning Control Of Complex Quantum Systems Using Differential Evolution With Mixed Strategies

Controlling quantum systems has become a fundamental task in the promising quantum technology,and it is relevant to many emerging areas such as atomic physics,molecular chemistry,and quantum information science.Some control methods,such as optimal control theory,Lyapunov control approaches and close-loop learning control have been developed for quantum systems.Among these methods,close-loop learning control is a powerful approach for complex quantum control tasks and has achieved great success in laser control of molecules.Close loop learning control is an effective learning method for designing optimal control of quantum systems,and its core lies in designing the learning algorithms.Gradient based methods are useful to generate a better solution in a local search way,whereas the control design is strictly limited by system models and gradient information,some complex quantum control problems may have local optimum.Differential evolution(DE)is a stochastic searching algorithm,is easy to implement with low space complexity,and have exhibited great performance for complex problems.In this paper,we present a differential evolution method featuring in equally mixed strategies(EMSDE),and apply it to the close-loop leaning control for complex quantum systems.Besides,we adopt the sampling based learning control(SLC)method and define an average performance function to design an optimal control strategy robust against certain ranges of uncertainties.To demonstrate the performance of the proposed EMSDE method,we investigate three classes of quantum control problems including open quantum ensembles,superconducting circuits with fluctuations as well as a quantum network consisting of three interacting qubits.Numerical results verify the effectiveness of the proposed EMSDE method when dealing with different quantum systems and show its potential for complex quantum systems.