Efficient quantum lattice gas automata

Abstract

This study presents a novel quantum algorithm for lattice gas automata simulation with a single time step, demonstrating logarithmic complexity in terms of $CX$ gates. The algorithm is composed of three main steps: collision, mapping, and propagation. A computational complexity analysis and a comparison using different error rates and number of shots are provided. Despite the impact of noise, our findings indicate that accurate simulations could be achieved already on current noisy devices. This suggests potential for efficient simulation of classical fluid dynamics using quantum lattice gas automata, conditional on advancements to expand the current method to multiple time steps and state preparation.