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arXiv · 2602.17303

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

Niccoló Fonio·Pierre Sagaut·Giuseppe Di Molfetta
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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 Burgers like equations while retaining only two lattice velocities. This approach opens a promising route toward embedding momentum conservation and advancing toward Navier Stokes dynamics in 2D, going beyond Frisch, Hasslacher and Pomeau (FHP) and lattice Boltzmann method (LBM) with a quantum native model. We highlight how the presented algorithm results more efficient in full state evolution than other quantum nonlinear solvers, nonetheless its advantages respect to classical lattice gas methods. Being this model between classical and quantum computation, it gives a unique perspective on simulating nonlinearities with quantum computers, confirming quantum lattice gas models as a crucial playground for quantum simulations of nonlinearities.

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Niccoló Fonio, Pierre Sagaut, Giuseppe Di Molfetta. 2026-09-15. Two-dimensional quantum lattice gas algorithm for anisotropic Burger-like equations. https://doi.org/10.1103/34zq-6m8d

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