Bridging quantum and classical computing for partial differential equations through multifidelity machine learning

TL;DR

This paper presents a multifidelity machine learning framework that enhances coarse quantum PDE solutions with classical data to achieve high-fidelity results, enabling practical quantum computing applications in scientific physics despite hardware limitations.

Contribution

It introduces a novel multifidelity neural architecture that corrects low-fidelity quantum PDE solutions using sparse classical data, bridging the gap between quantum hardware constraints and scientific computing needs.

Findings

Successfully corrects coarse quantum PDE predictions.

Achieves accurate temporal extrapolation beyond training window.

Reduces need for high-fidelity quantum simulations.

Abstract

Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate long-time integration. These hardware bottlenecks confine quantum PDE solvers to low-fidelity regimes despite their theoretical potential for computational speedup. We introduce a multifidelity learning framework that corrects coarse quantum solutions to high-fidelity accuracy using sparse classical training data, facilitating the path toward practical quantum utility for scientific computing. The approach trains a low-fidelity surrogate on abundant quantum solver outputs, then learns correction mappings through a multifidelity neural architecture that balances linear and nonlinear transformations. Demonstrated on benchmark nonlinear PDEs including viscous Burgers equation and incompressible Navier-Stokes flows via quantum lattice Boltzmann methods, the framework successfully corrects coarse quantum predictions and achieves temporal extrapolation well beyond the classical training window. This strategy illustrates how one can reduce expensive high-fidelity simulation requirements while producing predictions that are competitive with classical accuracy. By bridging the gap between hardware-limited quantum simulations and application requirements, this work establishes a pathway for extracting computational value from current quantum devices in real-world scientific applications, advancing both algorithm development and practical deployment of near-term quantum computing for computational physics.