A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This work introduces a model of distributed computation for arbitrary graphs inspired by quantum cellular automata. As a by-product, we show how this model can reproduce the dynamic of a quantum walk on graphs. In this context, we investigate the communication cost for two interaction schemes. Finally, we explain how this particular quantum walk can be applied to solve the search problem and present numerical results on different types of topologies.

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