State transfer on two-fold Cayley trees via quantum walks

doi:10.1088/1674-1056/abcfa1

Abstract Perfect state transfer (PST) has great significance due to its applications in quantum information processing and quantum computation. The main problem we study in this paper is to determine whether the two-fold Cayley tree, an extension of the Cayley tree, admits perfect state transfer between two roots using quantum walks. We show that PST can be achieved by means of the so-called nonrepeating quantum walk [Phys. Rev. A 89 042332 (2014)] within time steps that are the distance between the two roots; while both the continuous-time quantum walk and the typical discrete-time quantum walk with Grover coin approaches fail. Our results suggest that in some cases the dynamics of a discrete-time quantum walk may be much richer than that of the continuous-time quantum walk.

Keywords: perfect state transfer two-fold Cayley tree quantum walk

Received: 23 September 2020
Revised: 03 November 2020
Accepted manuscript online: 02 December 2020

PACS:	03.67.Ac	(Quantum algorithms, protocols, and simulations)
	03.67.Lx	(Quantum computation architectures and implementations)
	03.67.Hk	(Quantum communication)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61802002 and 61701004), the Natural Science Foundation of Anhui Province, China (Grant No. 1708085MF162), and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20171458).

Corresponding Authors: ^†Corresponding author. E-mail: stmxue@163.com

Cite this article:

Xi-Ling Xue(薛希玲) and Yue Ruan(阮越) State transfer on two-fold Cayley trees via quantum walks 2021 Chin. Phys. B 30 020304

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