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

• URL: http://arxiv.org/abs/2212.00546v1
• Date: Thu, 1 Dec 2022 14:52:49 GMT
• Title: Quantum walk based state transfer algorithms on the complete M-partite graph
• Authors: Stanislav Skoupy and Martin Stefanak
• Abstract summary: We investigate coined quantum walk search and state transfer algorithms, focusing on the complete $M$-partite graph with $N$ vertices in each partition. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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