XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019
VIII School on Geometry and Physics 24-28.06.2019

Stanislav Skoupý

State transfer by means of discrete-time quantum walks

We introduce the scheme of discrete-time quantum walk algorithm for the state transfer on highly symmetric graphs with two marked vertices, sender and receiver. We consider the state transfer algorithm based on modified discrete-time quantum walk with coins search algorithm. We show how to simplify the calculation by finding the invariant subspace of the walk with respect to the evolution operator of the walk. We calculate the number of steps and we prove that the perfect state transfer is achieved on the star graph, on the complete bipartite graph and on the complete graph with one self loop at each vertex. The number of steps of the walk for each case scale as $O(\sqrt{N})$ where $N$ is number of vertices.

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