Quantum-Assisted Learning of Time-Dependent Parabolic PDEs

TL;DR

This paper introduces a hybrid quantum-classical method using variational circuits to solve time-dependent parabolic PDEs, demonstrating promising accuracy and resource efficiency for heat equations in 1D and 2D.

Contribution

It extends the QPINN approach to a broader class of PDEs, showcasing a practical quantum-assisted framework for scientific computing.

Findings

Accurately models heat equations in 1D and 2D

Effective under limited quantum resources

Potential for broader scientific computing applications

Abstract

We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic PDEs. To demonstrate its effectiveness, we focus on the 1D and 2D heat equations as representative examples and analyze its performance under constrained quantum resources. Our results show that the framework can accurately capture spatiotemporal dynamics, offering a promising direction for quantum-assisted scientific computing.