Topology and Holonomy in Discrete-time Quantum Walks
AbstractWe 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
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Puentes, G. Topology and Holonomy in Discrete-time Quantum Walks. Crystals 2017, 7, 122.
Puentes G. Topology and Holonomy in Discrete-time Quantum Walks. Crystals. 2017; 7(5):122.Chicago/Turabian Style
Puentes, Graciana. 2017. "Topology and Holonomy in Discrete-time Quantum Walks." Crystals 7, no. 5: 122.
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