On a neural network approach for solving potential control problem of the semiclassical Schrödinger equation

Abstract

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schrödinger equation, where the control variable is the potential given by an external field that may contain uncertainties. Inspired by a relevant work Li et al., 2021 [1], we incorporate the sampling-based learning process into the training of networks, while combining with the fast time-splitting spectral method for the Schrödinger equation in the semi-classical regime. The numerical results have shown the efficiency and accuracy of our proposed deep learning approach.