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arXiv · 2212.00546

Quantum walk based state transfer algorithms on the complete M-partite graph

Stanislav Skoupy·Martin Stefanak
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Abstract

We investigate coined quantum walk search and state transfer algorithms, focusing on the complete $M$-partite graph with $N$ vertices in each partition. First, it is shown that by adding a loop to each vertex the search algorithm finds the marked vertex with unit probability in the limit of a large graph. Next, we employ the evolution operator of the search with two marked vertices to perform a state transfer between the sender and the receiver. We show that when the sender and the receiver are in different partitions the algorithm succeeds with fidelity approaching unity for a large graph. However, when the sender and the receiver are in the same partition the fidelity does not reach exactly one. To amend this problem we propose a state transfer algorithm with an active switch, whose fidelity can be estimated based on the single vertex search alone.

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Stanislav Skoupy, Martin Stefanak. 2022-12-01. Quantum walk based state transfer algorithms on the complete M-partite graph. https://doi.org/10.1103/physreva.103.042222

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