Entanglement as a Structural Prior: Comparative Analysis of Separable and Entangled Quantum Physics-Informed Neural Networks for Coupled Power System Dynamics

Abstract

This paper provides a detailed comparison of the performance of separable and entangled Quantum Physics-Informed Neural Networks (QPINNs) to solve coupled nonlinear differential equations, with the multi-generator power system swing equation serving as a test application. Previous studies focused on single-layer circuits not enforcing initial conditions, while the work here implements multi-layer variational circuits that include explicit initial condition loss. All models are tested against both a high-accuracy RK45 numerical baseline and iso-parameter classical PINNs. An ablation study considering qubit count and circuit depth shows that entanglement is the most important architectural property because it provides approximately 10× lower physics residuals than separable QPINNs at equivalent parameter budgets for entangled QPINNs. An additional study of performance based on the number of generators shows the differential between performance of entangled QPINNs and classical PINNs becomes smaller as the system grows larger (40 machines for 2 machines and 27 machines for 4 machines). This supports the theory that a ring CNOT topology replicates physical connection between generators. This research demonstrates that entangled QPINNs are suitable candidates for power system stability analysis on NISQ hardware with 280× fewer parameters than classical PINNs with the same architecture.