JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (1): 52-59.doi: 10.6040/j.issn.1671-9352.0.2020.340

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2-Tessellable staggered quantum walk on finite even cycles

YANG Guang-bo, WANG Cai-shi, LUO Yan, WANG Yan-yan, NAN Xue-qi   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-01-05

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Abstract: A 2-tessellable staggered quantum walk is considered on finite even cycles, its evolution matrix is obtained, and properties of the matrix are analyzed. The probability distributions of 2-tessellable staggered quantum walk on 4-cycle are given. A comparison is made between 2-tessellable staggered quantum walk and the classical random walk.

Key words: staggered quantum walk, clique, graph tessellation cover, unitary matrix, probability distribution

CLC Number: 

  • O211.4
[1] AHARONOV Y, DAVIDOVICH L, ZAGURY N. Quantum random walks[J]. Physical Review A, 1993, 48(2):1687-1690.
[2] VENEGAS ANDRACA S E. Quantum walks: a comprehensive review[J]. Quantum Inf Process, 2012, 11(5):1015-1106.
[3] PORTUGAL R, SANTOS R A M, FERNANDES T D, et al. The staggered quantum walk model[J]. Quantum Inf Process, 2016, 15(1):85-101.
[4] PORTUGAL R. Staggered quantum walks on graphs[J]. Physical Review A, 2016, 93(6):1-13.
[5] KONNO N, SATO I, SEGAWA E. The spectra of the unitary matrix of a 2-tessellable staggered quantum walk on a graph[EB/OL].(2017)[2020]. https://arxiv.org/abs/1701.08274v1.
[6] KONNO N, IDE Y, SATO I. The spectral analysis of the unitary matrix of a 2-tessellable staggered quantum walk on a graph[J]. Linear Algebra and Its Applications, 2018, 545: 207-225.
[7] HIGUCHI Y, PORTUGAL R, SATO I. Eigenbasis of the evolution operator of 2-tessellable quantum walks[J]. Linear Algebra and Its Applications, 2019, 583:257-281.
[8] PORTUGAL R. Quantum walks and search algorithms[M]. 2nd ed. Berlin: Springer, 2018.
[9] BIGGS N. Algebraic graph theory[M]. Cambridge: Cambridge University Press, 1974.
[10] CHAGAS B, PORTUGAL R, BOETTCHER S, et al. Staggered quantum walk on hexagonal lattices[J]. Physical Review A, 2018, 98(5):1-8.
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