
Unveiling hidden topological phases of a onedimensional Hadamard quantum walkUnveiling hidden topological phases of a onedimensional Hadamard quantum walkAA11187113 
"/Obuse, Hideaki/"Obuse, Hideaki ,
"/Asbóth, János K./"Asbóth, János K. ,
"/Nishimura, Yuki/"Nishimura, Yuki ,
"/Kawakami, Norio/"Kawakami, Norio
92
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4
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20150723 , American Physical Society
ISSN:10980121
NCID:AA11187113
Description
Quantum walks, whose dynamics is prescribed by alternating unitary coin and shift operators, possess topological phases akin to those of Floquet topological insulators, driven by a timeperiodic field. While there is ample theoretical work on topological phases of quantum walks where the coin operators are spin rotations, in experiments a different coin, the Hadamard operator, is often used instead. This was the case in a recent photonic quantum walk experiment, where protected edge states were observed between two bulks whose topological invariants, as calculated by the standard theory, were the same. This hints at a hidden topological invariant in the Hadamard quantum walk. We establish a relation between the Hadamard and the spin rotation operator, which allows us to apply the recently developed theory of topological phases of quantum walks to the onedimensional Hadamard quantum walk. The topological invariants we derive account for the edge state observed in the experiment; we thus reveal the hidden topological invariant of the onedimensional Hadamard quantum walk.
FullText
http://repository.kulib.kyotou.ac.jp/dspace/bitstream/2433/202048/1/PhysRevB.92.045424.pdf