Applicability of solving the one- and two-dimensional Poisson equation with the quantum Harrow-Hassidim-Lloyd algorithm
File(s)
Published version
Author(s)
Ghafourpour, Luca
Laizet, Sylvain
Type
Journal Article
Abstract
This paper assesses the numerical accuracy of the Harrow-Hassidim-Lloyd (HHL) algorithm in solving a finite difference approximation of the Poisson equation, where the Thomas algorithm is used as a comparative benchmark. In the one-dimensional setting with homogeneous boundary conditions, the HHL algorithm exhibits numerical accuracy comparable to the Thomas algorithm. However, the HHL algorithm exhibits increased sensitivity to variations in input parameters for simulations with non-homogeneous boundary conditions. While the current implementation of the HHL algorithm is limited to solving the one-dimensional Poisson equation, we propose a novel hybrid framework to extend the applicability of the HHL algorithm to solving the two-dimensional Poisson equation. Our results show that although both algorithms perform similarly for small systems of 8×8 mesh nodes, the HHL algorithm shows increased input parameter sensitivity for systems of 16×16 mesh nodes, indicating that further development is needed to scale the hybrid approach effectively.
Date Issued
2025-08-01
Date Acceptance
2025-07-01
Citation
Physical Review Applied, 2025, 24 (2)
ISSN
2331-7019
Publisher
American Physical Society
Journal / Book Title
Physical Review Applied
Volume
24
Issue
2
Copyright Statement
Subject to copyright. This paper is embargoed until publication. Once published the Version of Record (VoR) will be available on immediate open access.
Publication Status
Published
Article Number
024032
Date Publish Online
2025-08-13