A 1D adaptive integer lattice gas with velocity-dependent collision fractions reproduces lattice Boltzmann equilibrium and cosine-wave dynamics, and can be encoded in log(N)+3 qubits with a linear collision operator.
Succi, The lattice Boltzmann equation: for fluid dy- namics and beyond (Oxford university press, 2001)
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Adaptive Lattice Gas Algorithm: Classical and Quantum implementations
A 1D adaptive integer lattice gas with velocity-dependent collision fractions reproduces lattice Boltzmann equilibrium and cosine-wave dynamics, and can be encoded in log(N)+3 qubits with a linear collision operator.