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arXiv:2602.17303 · Physical Review A

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

Niccoló Fonio, Pierre Sagaut, Giuseppe Di Molfetta

quant-phSubmitted Feb 19, 2026• Announced Feb 20, 2026• 0 citations
v1 · Feb 19, 2026v2 · Sep 15, 2026
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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.

DOI
10.1103/34zq-6m8d

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We analyze one-dimensional classical and quantum microscopic lattice-gas models governed by a lattice Boltzmann equation at the mesoscopic scale, achieved by ensemble averaging over microscopic realizations. The models are governed by the Burgers equation at the macroscopic scale, achieved by taking the limit where the grid size and time step both approach zero and by performing a perturbative Chapman-Enskog expansion. The quantum algorithm exploiting superposition and entanglement is more efficient than the classical one because the quantum algorithm requires less memory. Furthermore, its viscosity can be made arbitrarily small.