Unitary Quantum Algorithm for the Lattice-Boltzmann Method

TL;DR

This paper introduces a quantum algorithm for fluid dynamics simulations using the Lattice-Boltzmann method, enabling multiple time step computations and capturing non-linearity with potential quantum speedups.

Contribution

It presents a novel quantum encoding and collision operator for Lattice-Boltzmann, extending quantum simulation capabilities to non-linear fluid dynamics.

Findings

Successfully solves 1D advection-diffusion of Gaussian hill

Enables multiple time step simulation in linearized case

Captures non-linearity in quantum fluid dynamics model

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.