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

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.

💡 Research Summary

This paper revisits the hybrid quantum lattice gas (QLG) algorithm originally proposed by Yépez and extends it to a two‑dimensional (2D) setting capable of simulating anisotropic Burgers‑like equations while using only two lattice velocities per spatial direction. The authors first re‑derive the viscosity expression for the one‑dimensional (1D) Q‑D1Q2 model, correcting an approximation made in the original work. By parametrizing the unitary collision operator with three real angles (θ, ζ, ξ) and introducing the composite parameter α = cot θ cos(ζ − ξ), they obtain an exact formula for the macroscopic viscosity:

ν = −(δx)²/(2 δt) ·