Classical-quantum hybrid architecture for physics-informed neural networks
Phys. Rev. A 113, 042446 – Published 20 April, 2026
DOI: https://doi.org/10.1103/fdd3-qz1s
Abstract
In this work, we introduce the quantum-classical hybrid physics-informed neural network with multiplicative and additive couplings (QPINN-MAC): a novel hybrid architecture that integrates the framework of physics-informed neural networks (PINNs) with that of quantum neural networks (QNNs). Specifically, we prove that through strategic couplings between classical and quantum components, the QPINN-MAC retains the universal approximation property, ensuring its theoretical capacity to represent complex solutions of ordinary differential equations (ODEs). Simultaneously, we demonstrate that the hybrid QPINN-MAC architecture actively mitigates the barren-plateau problem, regions in parameter space where cost-function gradients decay exponentially with circuit depth, a fundamental obstacle in QNNs that hinders optimization during training. Furthermore, we prove that these couplings prevent gradient collapse, ensuring trainability even in high-dimensional regimes. We empirically validate these theoretical findings through computational simulations of a coupled resistor-inductor-capacitor circuit, demonstrating the superior accuracy and convergence of our hybrid architecture (QPINN-MAC) when compared with both classical (PINN) and purely quantum (standard QPINN) approaches. Thus, our results establish a new pathway for constructing quantum-classical hybrid models with theoretical convergence guarantees, which are essential for the practical application of QPINNs.
