Quantum Lattice Kinetic Scheme for Solving Two-dimensional and Three-dimensional Incompressible Flows

TL;DR

This paper introduces a quantum lattice kinetic scheme that allows flexible viscosity adjustment in quantum lattice Boltzmann methods, enabling accurate simulation of 2D and 3D incompressible flows with arbitrary Reynolds numbers.

Contribution

It proposes a novel quantum lattice kinetic scheme with a parameter for viscosity control, overcoming previous fixed mesh size limitations in quantum LBMs.

Findings

Quantum LKS achieves accuracy comparable to classical methods.

The scheme successfully simulates 2D and 3D flows like Taylor-Green vortex.

It enables simulations at arbitrary Reynolds numbers.

Abstract

Lattice Boltzmann method (LBM) is particularly well-suited for implementation on quantum circuits owing to its simple algebraic operations and natural parallelism. However, most quantum LBMs fix $\tau$ = 1 to avoid nonlinear collision, which restricts the simulation to a fixed mesh size for a given Reynolds number. To preserve the simplicity of setting $\tau$ = 1 while enhancing flexibility, we propose a quantum lattice kinetic scheme (LKS) by introducing a constant parameter $A$ into the equilibrium distribution function (EDF), enabling independent adjustment of the fluid's viscosity. This modification removes the constraint on mesh size, making it possible to simulate flows with arbitrary Reynolds numbers. The Chapman-Enskog analysis confirms the modified EDF still recovers the Navier-Stokes equations without compromising collision accuracy. We evaluate the method on 2D and 3D Taylor-Green vortex and lid-driven cavity flows, demonstrating that quantum LKS attains the same accuracy and convergence order as classical LKS. The first application of quantum LBM to 3D incompressible flows represents a significant step forward in large-scale fluid dynamics simulation.