Unitary Quantum Algorithm for the Lattice-Boltzmann Method
Abstract
We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium within a single time step. Our quantum algorithm enables the computation of multiple time steps in the linearized case, specifically for solving the advection-diffusion equation, before necessitating a full state measurement. Moreover, our formulation can be extended to compute the non-linear equilibrium distribution function for a single time step prior to measurement, utilizing the measurement as an essential algorithmic step. However, in the non-linear case, a classical postprocessing step is necessary for computing the moments of the distribution function. We validate our algorithm by solving the one dimensional advection-diffusion of a Gaussian hill. Our results demonstrate that our quantum algorithm captures non-linearity.
Cite
@article{arxiv.2405.13391,
title = {Unitary Quantum Algorithm for the Lattice-Boltzmann Method},
author = {David Wawrzyniak and Josef Winter and Steffen Schmidt and Thomas Indinger and Uwe Schramm and Christian Janßen and Nikolaus A. Adams},
journal= {arXiv preprint arXiv:2405.13391},
year = {2024}
}