Lattice Gas Cellular Automata (LGCA) is a classical numerical method widely known and applied to simulate several physical phenomena. Among these phenomena, we find fluid flows described by the Navier-Stokes equations. We develop a quantum algorithm that allows for the simulation of fluid dynamic LGCA on a quantum computer. Furthermore, we prove the conservation of the quantities of interest, but finding more quantum invariants than expected. Finally, we develop a phase estimation procedure for detecting quantities of interest such as mass and momentum, avoiding reinitialization of the cell. In addition, we discuss a sublinear encoding of the lattice which admits a unitary streaming but constrains the collision step.

翻译：格子气元胞自动机（LGCA）是一种经典数值方法，被广泛认知并应用于多种物理现象的模拟。在这些现象中，我们找到了由纳维-斯托克斯方程描述的流体流动。我们开发了一种量子算法，使得能够在量子计算机上模拟流体动力学LGCA。此外，我们证明了相关物理量的守恒性，但发现了比预期更多的量子不变量。最后，我们开发了一种相位估计程序，用于检测如质量和动量等关键物理量，避免了元胞的重新初始化。此外，我们讨论了一种允许酉流但约束碰撞步骤的格子亚线性编码方案。