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Notes on Inhomogeneous Quantum Walks

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arxiv 1104.2010 v2 pith:FB44OMWV submitted 2011-04-11 quant-ph cond-mat.dis-nncond-mat.stat-mechmath-phmath.MP

Yutaka Shikano , Hosho Katsura This is my paper · ORCID
classification quant-phcond-mat.dis-nncond-mat.stat-mechmath-phmath.MP
keywords inhomogeneousquantumwalksbutterflyclasscoinsdefineddiscrete-time
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We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which resembles the Hofstadter butterfly.

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  1. Singular continuous Cantor spectrum for magnetic quantum walks

    quant-ph 2019-08 accept novelty 7.0 of 10

    For irrational magnetic flux, the spectrum of the two-dimensional Hadamard magnetic quantum walk is a zero-measure Cantor set and the walk has no pure point spectrum, so the spectrum is purely singular continuous.

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