Lattice Gas Cellular Automata (LGCA) are a computational model widely known and applied for the simulation of many physical phenomena. Their implementation requires an amount of resources and operations which scale linearly versus the system size and number of time steps. We propose a quantum-pointers-based quantum algorithm able to simulate LGCA while exhibiting an exponential advantage in space complexity and a number of quantum operations independent from the system size. We propose a collision circuit for the FHP lattice-gas automata considering the 2-, 3-, and 4-body collisions. These are implemented with two methodologies that suggest the procedure for finding quantum circuits for LGCA with more collisions. We also propose a phase estimation algorithm to retrieve information about a single cell, whose application can be expanded for implementing other collisions. A general methodology to identify the invariants associated to quantum LGCA is also proposed.

翻译：格气元胞自动机（LGCA）是一种被广泛认知并应用于模拟多种物理现象的计算模型。其实现所需的资源与操作数量与系统规模和迭代步数呈线性关系。我们提出了一种基于量子指针的量子算法，能够在空间复杂度上实现指数级优势，且所需的量子操作数量与系统规模无关。针对FHP格气自动机，我们设计了包含二体、三体及四体碰撞的碰撞电路。这些碰撞通过两种方法实现，该方法可为具有更多碰撞的LGCA寻找量子电路提供参考。我们还提出了一种相位估计算法，用于提取单个元胞的信息，其应用可扩展到实现其他碰撞场景。此外，本文还提出了一种通用的方法学，用于识别量子LGCA的相关不变量。