Learning-Based Quantum Robust Control: Algorithm, Applications, and Experiments

Abstract

Robust control design for quantum systems has been recognized as a key task in quantum information technology, molecular chemistry and atomic physics. In this paper, an improved differential evolution algorithm of msMS DE is proposed to search robust fields for various quantum control problems. In msMS DE, multiple samples are used for fitness evaluation and a mixed strategy is employed for mutation operation. In particular, the msMS DE algorithm is applied to the control problem of open inhomogeneous quantum ensembles and the consensus problem of a quantum network with uncertainties. Numerical results are presented to demonstrate the excellent performance of the improved DE algorithm for these two classes of quantum robust control problems. Furthermore, msMS DE is experimentally implemented on femtosecond laser control systems to generate good signals of twophoton absorbtion and control fragmentation of halomethane molecules CH 2 BrI. Experimental results demonstrate excellent performance of msMS DE in searching effective femtosecond laser pulses for various tasks.

Learning Control of Quantum Systems

“…The robust control of quantum systems has been recognized as a key task in developing practical quantum technology since the existence of noise and uncertainties is unavoidable. Learning control is an effective candidate for achieving robust performance in some quantum control problems (Dong et al 2020). We first consider the control problem of inhomogeneous quantum ensembles.…”

“…In other applications where we need to enhance the robustness in closed-loop learning control, we may either use the Hessian matrix information (Xing et al 2014) or integrate the idea of SLC into the learning algorithm in searching for robust control fields. For example, an improved DE algorithm (called as msMS DE) has been proposed to search for robust femtosecond laser pulses to control fragmentation of the molecule CH 2 BrI (Dong et al 2020). In msMS DE, multiple samples are used for fitness evaluation and a mixed strategy is employed for the mutation operation.…”

“…A few results on the controllability of open quantum systems have also been presented. For control law design, optimal control theory (Dong and Petersen 2010), Lyapunov control approaches (Kuang et al 2017), learning control algorithms (Rabitz et al 2000), and robust control methods (Dong et al 2020) have been developed in manipulating quantum systems for achieving various control objectives.…”

“…For these situations, stochastic search algorithms usually have improved performance to find a good control field. The genetic algorithm (GA) and differential evolution (DE) (Dong et al 2020) have been widely used in the area of quantum control of molecular systems and achieved great success (Rabitz et al 2000). Another task in quantum control is to achieve robustness performance in quantum systems.…”

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

“…One can employ machine learning methods [15][16][17][18][19][20][21] to deal with this problem. Another promising approach to tackle this problem is to apply gradient-free algorithms, for example, Nelder-Mead algorithm (NM) [22,23] and differential evolution algorithm (DE) [5,6,[24][25][26].…”