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A quantum advection-diffusion solver using the quantum singular value transform
Gard Olav Helle, Tommaso Benacchio, Anna Bomme Ousager, Jørgen Ellegaard Andersen·December 16, 2025
Quantum Physics
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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.