Quantum-Enhanced Convergence of Physics-Informed Neural Networks

TL;DR

This paper demonstrates that hybrid quantum-classical neural networks can solve complex PDEs more efficiently than classical methods, reducing training epochs needed for accurate solutions.

Contribution

It introduces hybrid quantum-classical neural networks for PDE solving and systematically shows their advantage over classical networks in training efficiency.

Findings

Quantum-enhanced networks achieve accurate PDE solutions faster.

Hybrid networks outperform classical networks on complex problems.

Fewer training epochs needed with quantum components.

Abstract

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to accelerate the solution of PDEs is promising, but not competitive with numerical solvers yet. Here, we show how quantum computing can improve the ability of physics-informed neural networks to solve partial differential equations. For this, we develop hybrid networks consisting of quantum circuits combined with classical layers and systematically test them on various non linear PDEs and boundary conditions in comparison with purely classical networks. We demonstrate that the advantage of using quantum networks lies in their ability to achieve an accurate approximation of the solution in substantially fewer training epochs, particularly for more complex problems. These findings provide the basis for targeted developments of hybrid quantum neural networks with the goal to significantly accelerate numerical modeling.