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

• URL: http://arxiv.org/abs/2512.22163v1
• Date: Tue, 16 Dec 2025 19:06:27 GMT
• Title: A quantum advection-diffusion solver using the quantum singular value transform
• Authors: Gard Olav Helle, Tommaso Benacchio, Anna Bomme Ousager, Jørgen Ellegaard Andersen,
• Abstract summary: We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators.<n>Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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