Robust Control of Uncertain Quantum Systems based on Physics-informed Neural Networks and Sampling Learning

High-fidelity quantum control is one of the key elements in quantum computing and information processing. In view of possible inaccuracies in quantum system modeling and inevitable errors in control fields, the design of robust control fields is of great importance. In this paper, we propose a neural network-based robust control strategy that incorporates physics-informed neural networks (PINNs) and sampling-based learning control techniques for uncertain closed and open quantum systems. We employ the gradient descent algorithm with momentum for the network training, where two methods including direct calculation and automatic differentiation are used to compute the gradient of the loss function with respect to network weights. The direct calculation method demonstrates the internal mechanism of the gradient computation, while the automatic differentiation technology is easier to utilize. We provide some guidelines for the parameter selection of the sampling learning algorithm in the PINN robust control scheme to ensure good control performance. In particular, for open quantum systems with uncertainties, we point out the necessity of fast control. Some simulation experiments are conducted on closed and open systems with uncertainties and the results show the effectiveness of the proposed PINN control scheme in achieving high-fidelity state transfer of uncertain quantum systems.