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 Schr\"odinger equation, where the control variable is the potential given by an external field that may contain uncertainties. Inspired by a relevant work [29], we incorporate the sampling-based learning process into the training of networks, while combining with the fast time-splitting spectral method for the Schr\"odinger equation in the semiclassical regime. The numerical results have shown the efficiency and accuracy of our proposed deep learning approach.

翻译：量子系统的鲁棒控制设计是实用技术中的关键挑战。本研究将神经网络应用于半经典薛定谔方程的控制问题学习，其中控制变量为可能包含不确定性的外场势能。受相关工作[29]启发，我们将基于采样的学习过程融入网络训练，同时结合快速时间分裂谱方法处理半经典区域的薛定谔方程。数值结果表明，所提出的深度学习方法具有良好的效率与准确性。