A Symplectic Based Neural Network Algorithm for Quantum Controls under Uncertainty

Abstract

Robust quantum control with uncertainty plays a crucial role in practical quantum technologies. This paper presents a method for solving a quantum control problem by combining neural network and symplectic finite difference methods. The neural network approach provides a framework that is easy to establish and train. At the same time, the symplectic methods possess the norm-preserving property for the quantum system to produce a realistic solution in physics. We construct a general high dimensional quantum optimal control problem to evaluate the proposed method and an approach that combines a neural network with forward Euler’s method. Our analysis and numerical experiments confirm that the neural network-based symplectic method achieves significantly better accuracy and robustness against noises.