Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics

TL;DR

This paper introduces a quantum lattice Boltzmann method for simulating nonlinear fluid dynamics, combining lattice gas and Boltzmann approaches, validated on large-scale turbulence benchmarks, advancing quantum algorithms for nonlinear systems.

Contribution

A novel quantum lattice Boltzmann algorithm that efficiently simulates nonlinear fluid flows using linear quantum operations and a node-level ensemble description.

Findings

Accurately simulates vortex merging and turbulence on large grids

Demonstrates agreement with classical direct numerical simulations

Provides insights into quantum algorithm development for nonlinear problems

Abstract

Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for nonlinear problems remains a significant challenge. We introduce a novel node-level ensemble description of lattice gas for simulating nonlinear fluid dynamics on a quantum computer. This approach combines the advantages of the lattice Boltzmann method, which offers low-dimensional representation, and lattice gas cellular automata, which provide linear collision treatment. Building on this framework, we propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality. We validated the algorithm through comprehensive simulations of benchmark cases, including vortex-pair merging and decaying turbulence on $2048^2$ computational grid points. The results demonstrate remarkable agreement with direct numerical simulation, effectively capturing the essential nonlinear mechanisms of fluid dynamics. This work offers valuable insights into developing quantum algorithms for other nonlinear problems, and potentially advances the application of quantum computing across various transport phenomena in engineering.