Quantum Codes for Topological Quantum Comp...

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Beschreibung

This book offers a structured algebraic and geometric approach to the classification and construction of quantum codes for topological quantum computation. It combines key concepts in linear algebra, algebraic topology, hyperbolic geometry, group theory, quantum mechanics, and classical and quantum coding theory to help readers understand and develop quantum codes for topological quantum computation.

One possible approach to building a quantum computer is based on surface codes, operated as stabilizer codes. The surface codes evolved from Kitaev's toric codes, as a means to developing models for topological order by using qubits distributed on the surface of a toroid. A significant advantage of surface codes is their relative tolerance to local errors. A second approach is based on color codes, which are topological stabilizer codes defined on a tessellation with geometrically local stabilizer generators. This book provides basic geometric concepts, like surface geometry, hyperbolic geometry and tessellation, as well as basic algebraic concepts, like stabilizer formalism, for the construction of the most promising classes of quantum error-correcting codes such as surfaces codes and color codes.

The book is intended for senior undergraduate and graduate students in Electrical Engineering and Mathematics with an understanding of the basic concepts of linear algebra and quantum mechanics.

Über den Autor

Clarice Dias de Albuquerque is an adjoint professor at the Federal University of Cariri, Brazil. She holds Bachelor's and Master's degrees from the Federal University of Ceará, Brazil, and a PhD in Electrical Engineering from the State University of Campinas, Brazil.

Eduardo Brandani da Silva is an Associate Professor at the State University of Maringá, Brazil. He holds Bachelor's (1988) and Master's degrees (1992) in Mathematics from the State University of Campinas, Brazil, and a PhD in Electrical Engineering (2000) from the same university.

Waldir Silva Soares Júnior is a Professor at the Federal Technological University of Paraná, Brazil. He holds Bachelor's (2004) and Master's degrees (2008) in Mathematics from the State University of Maringá, and a PhD in Mathematics (2017) from the same university.

Zusammenfassung

Offers a structured algebraic and geometric approach

Describes quantum codes in detail using a step-by-step approach

Presents key concepts in linear algebra, algebraic topology, hyperbolic geometry, group theory, quantum mechanics

Inhaltsverzeichnis

Introduction.- Review of Mathematical Concepts.- Topological Quantum Codes.- Color Codes.- The Interplay between Color Codes and Toric Codes.

Details

Erscheinungsjahr:	2022
Fachbereich:	Theoretische Physik
Genre:	Physik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	SpringerBriefs in Mathematics
Inhalt:	viii 116 S. 11 s/w Illustr. 19 farbige Illustr. 116 p. 30 illus. 19 illus. in color.
ISBN-13:	9783031068324
ISBN-10:	3031068327
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Albuquerque, Clarice Dias de Soares Jr., Waldir Silva Silva, Eduardo Brandani Da
Auflage:	1st ed. 2022
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG SpringerBriefs in Mathematics
Maße:	235 x 155 x 8 mm
Von/Mit:	Clarice Dias de Albuquerque (u. a.)
Erscheinungsdatum:	05.08.2022
Gewicht:	0,201 kg

Artikel-ID: 121443579