Journal Article

A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods

Ellison, Elizabeth, Davis, Noah, Loveland, Mark, Trahan, Corey Jason

2023

Overview

Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations.

• Publisher: MDPI AG,MDPI
• Subject: Algorithms / Artificial intelligence / Circuits / Cloud computing / Computers / Data compression / Differential equations / Finite element method / finite-element methods / heat equation / Industry standards / Integrated circuits / Machine learning / Methods / NMR / Noise control / Nuclear magnetic resonance / Partial differential equations / Poisson equation / Probability distribution / quantum algorithms / Quantum computing / quantum variational algorithm / Random variables / Semiconductor chips / Solvers / Supercomputers / Wave equations