Topology and holonomy in discrete-time quantum walks

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 sys...

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Autor principal: Puentes, G.
Formato: JOUR
Materias:
Holonomy
Quantum walks
Topology
Zak phase
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_20734352_v7_n5_p_Puentes
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_20734352_v7_n5_p_Puentes
record_format dspace
spelling todo:paper_20734352_v7_n5_p_Puentes2023-10-03T16:39:10Z Topology and holonomy in discrete-time quantum walks Puentes, G. Holonomy Quantum walks Topology Zak phase 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. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. Fil:Puentes, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_20734352_v7_n5_p_Puentes
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Holonomy
Quantum walks
Topology
Zak phase
spellingShingle Holonomy
Quantum walks
Topology
Zak phase
Puentes, G.
Topology and holonomy in discrete-time quantum walks
topic_facet Holonomy
Quantum walks
Topology
Zak phase
description 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. © 2017 by the authors. Licensee MDPI, Basel, Switzerland.
format JOUR
author Puentes, G.
author_facet Puentes, G.
author_sort Puentes, G.
title Topology and holonomy in discrete-time quantum walks
title_short Topology and holonomy in discrete-time quantum walks
title_full Topology and holonomy in discrete-time quantum walks
title_fullStr Topology and holonomy in discrete-time quantum walks
title_full_unstemmed Topology and holonomy in discrete-time quantum walks
title_sort topology and holonomy in discrete-time quantum walks
url http://hdl.handle.net/20.500.12110/paper_20734352_v7_n5_p_Puentes
work_keys_str_mv AT puentesg topologyandholonomyindiscretetimequantumwalks
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