Simulating non-trivial incompressible flows with a quantum lattice Boltzmann algorithm

TL;DR

This paper extends a quantum lattice Boltzmann algorithm to simulate realistic incompressible fluid flows, analyzing its complexity and demonstrating its accuracy through classical simulations of key flow scenarios, paving the way for quantum CFD advancements.

Contribution

It introduces modifications to a quantum LBM for realistic boundary conditions and external forces, maintaining asymptotic scaling and potential quantum advantage.

Findings

The modified quantum LBM preserves asymptotic complexity.

Classical simulations confirm accuracy and convergence.

Framework established for complex flow configurations.

Abstract

Quantum algorithms have been identified as a potential means to accelerate computational fluid dynamics (CFD) simulations, with the lattice Boltzmann method (LBM) being a promising candidate for realizing quantum speedups. Here, we extend the recent quantum algorithm for the incompressible LBM to account for realistic fluid dynamics setups by incorporating walls, inlets, outlets, and external forcing. We analyze the associated complexity cost and show that these modifications preserve the asymptotic scaling, and potential quantum advantage, of the original algorithm. Moreover, to support our theoretical analysis, we provide a classical numerical study illustrating the accuracy, complexity, and convergence of the algorithm for representative incompressible-flow cases, including the driven Taylor-Green vortex, the lid-driven cavity flow, and the flow past a cylinder. Our results provide a pathway to accurate quantum simulation of nonlinear fluid dynamics, and a framework for extending quantum LBM to more challenging flow configurations.