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, Graciana
Publicado:	2017
Materias:	Holonomy Quantum walks Topology Zak phase
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20734352_v7_n5_p_Puentes 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	paper:paper_20734352_v7_n5_p_Puentes
record_format	dspace
spelling	paper:paper_20734352_v7_n5_p_Puentes2023-06-08T16:34:10Z Topology and holonomy in discrete-time quantum walks Puentes, Graciana 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. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20734352_v7_n5_p_Puentes 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, Graciana 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.
author	Puentes, Graciana
author_facet	Puentes, Graciana
author_sort	Puentes, Graciana
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
publishDate	2017
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20734352_v7_n5_p_Puentes http://hdl.handle.net/20.500.12110/paper_20734352_v7_n5_p_Puentes
work_keys_str_mv	AT puentesgraciana topologyandholonomyindiscretetimequantumwalks
_version_	1768542149529305088

Topology and holonomy in discrete-time quantum walks

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