Qade: Solving Differential Equations on Quantum Annealers

TL;DR

Qade introduces a quantum annealer-based method for solving differential equations by representing solutions as basis function combinations, demonstrating accuracy on current devices for small problems.

Contribution

The paper presents a novel general approach, Qade, for solving differential equations on quantum annealers, extending their application to linear systems with complex coefficients.

Findings

Quantum annealers can accurately solve small differential equations.

Qade effectively handles coupled PDEs with non-linear coefficients.

The method is implemented in an accessible Python package.

Abstract

We present a general method, called Qade, for solving differential equations using a quantum annealer. The solution is obtained as a linear combination of a set of basis functions. On current devices, Qade can solve systems of coupled partial differential equations that depend linearly on the solution and its derivatives, with non-linear variable coefficients and arbitrary inhomogeneous terms. We test the method with several examples and find that state-of-the-art quantum annealers can find the solution accurately for problems requiring a small enough function basis. We provide a Python package implementing the method at gitlab.com/jccriado/qade.