Quantum Physics-Informed Neural Networks for Maxwell’s Equations: Circuit Design, “Black Hole” Barren Plateaus Mitigation, and GPU Acceleration
Abstract
Abstract Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a Quantum Physics- Informed Neural Network (QPINN) framework is proposed to solve two-dimensional (2D) time-dependent Maxwell’s equations. Our approach utilizes a parameterized quantum circuit (PQC) in conjunction with the classical neural network architecture and enforces physical laws, including a global energy conservation principle, during training. A quantum simulation library was developed to efficiently compute circuit outputs and derivatives by leveraging GPU acceleration based on PyTorch, enabling end-to-end training of the QPINN. The method was evaluated on two 2D electromagnetic wave propagation problems: one in free space (vacuum) and one with a dielectric medium. Multiple quantum circuit ansätze, input scales, and an added loss term were compared in a thorough ablation study. Furthermore, recent techniques to enhance PINN convergence, including random Fourier feature embeddings and adaptive time-weighting, were incorporated. Our results demonstrate that the QPINN achieves accuracy comparable, and even greater than the classical PINN baseline, while using a significantly smaller number of trainable parameters. This study also shows that adding an energy conservation term to the loss stabilizes training and improves the…
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