A Stable and General Quantum Fractional-Step Lattice Boltzmann Method for Incompressible Flows

TL;DR

This paper introduces a quantum fractional-step lattice Boltzmann method that enhances stability and accuracy for simulating incompressible flows, including thermal flows, by combining quantum and classical computations.

Contribution

It develops a stable quantum LBM framework with a fractional-step approach, enabling high Reynolds number simulations and thermal flow modeling, which was not possible with previous quantum LBMs.

Findings

Achieves accuracy comparable to classical LBM

Demonstrates stability at high Reynolds numbers

First quantum simulation of 3D incompressible thermal flows

Abstract

Quantum computing shows substantial potential in accelerating simulations and alleviating memory bottlenecks in computational fluid dynamics (CFD), owing to its inherent properties of superposition and entanglement. The lattice Boltzmann method (LBM), being largely algebraic in nature, has inspired the development of various quantum LBMs. However, most existing approaches fix the relaxation time at $\tau$ = 1, thereby confining a given mesh resolution to simulations at a single Reynolds number. Although our earlier quantum lattice kinetic scheme (LKS) lifted this restriction, it suffers from instability at high Reynolds numbers. To address this challenge, we propose a quantum fractional-step LBM (FS-LBM). In this framework, the predictor step is implemented on a quantum circuit using the standard LBM formulation, while the corrector step is performed classically. The relaxation time is retained at $\tau$ = 1 to ensure seamless compatibility with existing quantum LBMs. Benchmark simulations of representative two- and three-dimensional incompressible isothermal and thermal flows demonstrate that the quantum FS-LBM achieves accuracy and convergence orders consistent with its classical counterpart, while significantly outperforming the quantum LKS in both precision and stability. Notably, this work presents the first quantum LBM simulation of three-dimensional incompressible thermal flows.