Two-dimensional quantum lattice gas algorithm for anisotropic Burger-like equations

TL;DR

This paper introduces a minimal 2D quantum lattice gas algorithm capable of simulating anisotropic Burger-like equations, refining viscosity predictions and paving the way for quantum simulations of Navier-Stokes dynamics.

Contribution

It presents a novel 2D generalization of the quantum lattice gas algorithm that efficiently models anisotropic fluid equations with momentum conservation.

Findings

Refined analytical and numerical viscosity predictions.

Successful simulation of anisotropic Burger-like equations.

Potential for quantum modeling of 2D Navier-Stokes equations.

Abstract

Building on hybrid quantum lattice gas algorithm, we revisit the possibilities of this quantum lattice model. By deriving a correction to the predicted viscosity, we provide analytical and numerical results that refine original formulation. We introduce a minimal 2D generalization of the algorithm, which allows to simulate anisotropic Burgerlike equations while retaining only two lattice velocities. This approach opens a promising route toward embedding momentum conservation and advancing toward NavierStokes dynamics in 2D, going beyond Frisch, Hasslacher and Pomeau (FHP) with a quantum native model.