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 two-dimensional generalization of the algorithm, which allows us to simulate anisotropic Burger-like equations while retaining only two lattice velocities. This approach opens a promising route toward embedding momentum conservation and advancing toward Navier-Stokestwo dynamics in two dimensions, going beyond Frisch, Hasslacher, and Pomeau and lattice Boltzmann method with a quantum native model. We highlight how the presented algorithm is more efficient for full state evolution than other quantum nonlinear solvers, nonetheless we clarify its advantages compared to classical lattice gas methods. Being that this model is 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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• Equilibrium lattice models
• Cellular automata
• Lattice-Boltzmann methods