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  • Open Access

Quantum algorithms for solving a drift-diffusion equation: A complexity analysis

Ellen Devereux* and Animesh Datta

  • *Contact author: Ellen.Devereux@warwick.ac.uk; Also at Fujitsu UK Ltd.
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Phys. Rev. A 112, 042419 – Published 14 October, 2025

DOI: https://doi.org/10.1103/1fw9-h14w

Abstract

We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare the complexities of these methods to their classical counterparts, finding that diagonalization via the quantum Fourier transform offers a quantum computational advantage for solving linear partial differential equations at a fixed final time. We employ a multidimensional amplitude estimation process to extract the full probability distribution from the quantum computer.

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Phys. Rev. A 112, 042419– Published 14 October, 2025
  • Received 3 June 2025
  • Accepted 25 August 2025
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