Quantum algorithm for smoothed particle hydrodynamics

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Au-Yeung, R. and Williams, A.J. and Kendon, V.M. and Lind, S.J. (2024) Quantum algorithm for smoothed particle hydrodynamics. Computer Physics Communications, 294. 108909. ISSN 0010-4655 (https://doi.org/10.1016/j.cpc.2023.108909)

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Abstract

We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation via an inner product of quantum registers. Using a one-dimensional function, we test the approach in a classical sense for the kernel sum and first and second derivatives of a one-dimensional function, using both the Gaussian and Wendland kernel functions, and compare various register sizes against analytical results. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the one-dimensional advection and diffusion partial differential equations, which are commonly encountered in fluids simulations. This work provides a foundation for a more general SPH algorithm, eventually leading to highly efficient simulations of complex engineering problems on gate-based quantum computers.

ORCID iDs

Au-Yeung, R. ORCID logoORCID: https://orcid.org/0000-0002-0082-5382, Williams, A.J., Kendon, V.M. ORCID logoORCID: https://orcid.org/0000-0002-6551-3056 and Lind, S.J.;
  • Item type:Article
    ID code:86751
    Dates:
    Date
    Event
    31 January 2024
    Published
    4 September 2023
    Published Online
    29 August 2023
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:22 Sep 2023 10:07
    Last modified:13 Nov 2024 12:07
    URI:https://strathprints.strath.ac.uk/id/eprint/86751
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