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Crystals 2017, 7(5), 122; doi:10.3390/cryst7050122

Topology and Holonomy in Discrete-time Quantum Walks

1
Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
2
3rd Institute of Physics, Research Center Scope and MPI for Solid State Research, University of Stuttgart, 70569 Stuttgart, Germany
Academic Editor: Helmut Cölfen
Received: 24 January 2017 / Revised: 28 March 2017 / Accepted: 18 April 2017 / Published: 28 April 2017
(This article belongs to the Special Issue Topological Crystalline Insulators: Current Progress and Prospects)
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Abstract

We present a research article which formulates the milestones for the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in parameter space. Unlike other similar systems recently studied in detail in the literature, this system does not present continous 1D topological boundaries, it only presents a discrete number of Dirac points where the quasi-energy gap closes. At these discrete points, the topological winding number is not defined. Therefore, such discrete points represent topological boundaries of dimension zero, and they endow the system with a non-trivial topology. We illustrate the non-trivial character of the system by calculating the Zak phase. We discuss the prospects of this system, we propose a suitable experimental scheme to implement these ideas, and we present preliminary experimental data. View Full-Text
Keywords: quantum walks; Zak phase; topology; holonomy quantum walks; Zak phase; topology; holonomy
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Puentes, G. Topology and Holonomy in Discrete-time Quantum Walks. Crystals 2017, 7, 122.

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