Variational quantum algorithm based on Lagrange polynomial encoding to solve differential equations
File(s)
Published version
Author(s)
Hunout, Josephine
Laizet, Sylvain
Iannucci, Lorenzo
Type
Journal Article
Abstract
Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are notoriously hard to solve, due to their intricate nature, and finding solutions to DEs often exceeds the capabilities of traditional computational approaches. Recent advances in quantum computing have triggered a growing interest from researchers for the design of quantum algorithms for solving DEs. In this work, we introduce two different architectures of a novel variational quantum algorithm (VQA) with Lagrange polynomial encoding in combination with derivative quantum circuits using the Hadamard test differentiation to approximate the solution of DEs. To demonstrate the potential of our new VQA, two well-known ordinary differential equations are used: the damped mass-spring system from a given initial condition and the Poisson equation for periodic, Dirichlet, and Neumann boundary conditions. It is shown that the proposed new VQA has a reduced gate complexity compared to previous variational quantum algorithms, for a similar or better quality of the solution.
Date Issued
2025-06-03
Date Acceptance
2025-04-24
Citation
Physical Review A: Atomic, Molecular and Optical Physics, 2025, 111 (6)
ISSN
1050-2947
Publisher
American Physical Society
Journal / Book Title
Physical Review A: Atomic, Molecular and Optical Physics
Volume
111
Issue
6
Copyright Statement
© 2025 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
License URL
Identifier
10.1103/PhysRevA.111.062404
Publication Status
Published
Article Number
ARTN 062404