Float Lattice Gas Automata: A connection between Molecular Dynamics and Lattice Boltzmann Method for quantum computers

Building upon the Integer Lattice Gas Automata framework of Blommel $\mathit{\text{et}}\mathit{\text{al.}}$ \cite{PhysRevE.97.023310}, we introduce a simplified, fluctuation-free variant. This approach relies on floating-point numbers and closely mirrors the Lattice Boltzmann Method (LBM), with the key distinction being a novel collision operator. This operator, derived from the ensemble average of transition probabilities, generates nonlinear terms. We propose this new Float Lattice Gas Automata (FLGA) collision as a computationally efficient alternative to traditional and quantum LBM implementations.