Quantum algorithm for the advection-diffusion equation by direct block encoding of the time-marching operator
File(s)
Published version
Author(s)
Over, Paul
Bengoechea, Sergio
Brearley, Peter
Laizet, Sylvain
Rung, Thomas
Type
Journal Article
Abstract
A quantum algorithm for simulating multidimensional scalar transport problems using a time marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic success probability of the squared solution norm without the need for amplitude amplification, thereby retaining a linear dependence on the simulation time.
The algorithm separates the explicit time-marching operator into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation and combined with the shift operator through the linear combination of unitaries algorithm. State vector simulations of a scalar transported in a steady two-dimensional Taylor-Green vortex support the theoretical findings.
The algorithm separates the explicit time-marching operator into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation and combined with the shift operator through the linear combination of unitaries algorithm. State vector simulations of a scalar transported in a steady two-dimensional Taylor-Green vortex support the theoretical findings.
Date Issued
2025-07-01
Date Acceptance
2025-06-04
Citation
Physical Review A: Atomic, Molecular and Optical Physics, 2025, 112 (1)
ISSN
1050-2947
Publisher
American Physical Society
Journal / Book Title
Physical Review A: Atomic, Molecular and Optical Physics
Volume
112
Issue
1
Copyright Statement
© The Author(s) 2025. 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/d8hb-fv93
Publication Status
Published
Article Number
L010401