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Paper detail

Periodicity for the Hadamard walk on cycles

The present paper treats the period T_N of the Hadamard walk on a cycle C_N with N vertices. Dukes (2014) considered the periodicity of more general quantum walks on C_N and showed T_2 =2, T_4=8, T_8=24 for the Hadamard walk case. We prove that the Hadamard walk does not have any period except for his case, i.e., N=2, 4, 8. Our method is based on a path counting and cyclotomic polynomials which is different from his approach based on the property of eigenvalues for unitary matrix that determines the evolution of the walk.

preprint2015arXivOpen access
Norio KonnoYuki ShimizuMasato Takei
math-phmath.PRmath.MPquant-ph
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Norio KonnoYuki ShimizuMasato Takei

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