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Lattice Gas Cellular Automata (LGCA) is a classical numerical method widelyknown and applied to simulate several physical phenomena. In this paper, westudy the translation of LGCA on quantum computers (QC) using computationalbasis encoding (CBE), developing methods for different purposes. In particular,we clarify and discuss some fundamental limitations and advantages in using CBEand quantum walk as streaming procedure. Using quantum walks affect thepossible encoding of classical states in quantum orthogonal states, featurelinked to the unitarity of collision and to the possibility of getting aquantum advantage. Then, we give efficient procedures for optimizingcollisional quantum circuits, based on the classical features of the model.This is applied specifically to fluid dynamic LGCA. Alongside, a new collisioncircuit for a 1-dimensional model is proposed. We address the important pointof invariants in LGCA providing a method for finding how many invariants appearin their QC formulation. Quantum invariants outnumber the classicalexpectations, proving the necessity of further research. Lastly, we prove thevalidity of a method for retrieving any quantity of interest based on quantumphase estimation (QPE).

Quantum collision circuit, quantum invariants and quantum phase estimation procedure for fluid dynamic lattice gas automata