A quantum advection-diffusion solver using the quantum singular value transform

Abstract:We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy. The theoretical results are supported by numerical simulations of one- and two-dimensional benchmarks.

arXiv:2512.22163 [quant-ph]

(or arXiv:2512.22163v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2512.22163 Focus to learn more arXiv-issued DOI via DataCite

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