A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search on regular graphs. This work introduces a new quantum walk-based searching scheme, designed to search nodes or edges on arbitrary graphs. As byproduct, such new model allows to generalise quantum cellular automata, usually defined on regular grids, to quantum anonymous networks, allowing a new physics-like mathematical environment for distributed quantum computing.

翻译：离散时间量子游走被视为量子元胞自动机的单粒子扇区。基于该数学框架的搜索问题长期受到学界关注，但现有成果多聚焦于规则图上的空间搜索。本文提出一种新型量子游走搜索方案，可对任意图结构中的节点或边进行搜索。该模型作为衍生成果，将通常定义在规则网格上的量子元胞自动机推广至量子匿名网络，为分布式量子计算提供了类物理的新型数学环境。