Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecasting

Abstract

We study a hybrid proposal--correction architecture for reduced-order PDE forecasting in which a pure-state quantum reservoir computer (QRC) predicts latent coefficient dynamics and a PINN-based physics-informed corrector (PIC) refines local rollout windows. The method is evaluated on Burgers and Kuramoto--Sivashinsky (KS), with KS as the primary chaotic benchmark. On KS, QRC+PIC consistently improves over QRC alone in RMSE, NRMSE, and PDE residual, while Burgers highlights a regime in which simple baselines remain strong. These results suggest that QRC proposals with local physics-informed correction are a viable benchmark-dependent reduced-order forecasting strategy.

11 pages, 5 figures. Accepted at QNRL@WCCI 2026. To appear in Advances in Quantum Neural and Reinforcement Learning, Communications in Computer and Information Science, vol. 3063, Springer Singapore, 2026