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Quantum algorithm for the advection-diffusion equation by direct block encoding of the time-marching operator
Citation Link: https://doi.org/10.15480/882.15368
Publikationstyp
Journal Article
Date Issued
2025-07-01
Sprache
English
TORE-DOI
Volume
112
Issue
1
Article Number
L010401
Citation
Physical Review A / Atomic, molecular, and optical physics 112 (1): L010401 (2025)
Publisher DOI
Publisher
American Physical Society (APS)
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.
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.
DDC Class
600: Technology
Publication version
publishedVersion
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