Quantum Codes for Topological Quantum Computation / by Clarice Dias de Albuquerque, Eduardo Brandani da Silva, Waldir Silva Soares Jr

By:

Albuquerque, Clarice Dias de [VerfasserIn]

Contributor(s):

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerBriefs in Mathematics | Springer eBook CollectionPublisher: Cham : Springer International Publishing, 2022Publisher: Cham : Imprint: Springer, 2022Edition: 1st ed. 2022Description: 1 Online-Ressource(VIII, 116 p. 30 illus., 19 illus. in color.)ISBN:

9783031068331

Subject(s):

Additional physical formats: 9783031068324 | 9783031068348 | Erscheint auch als: Quantum codes for topological quantum computation. Druck-Ausgabe Cham, Switzerland : Springer Nature, 2022. viii, 116 SeitenDDC classification:

006.3843 23
530.12 23

DOI: DOI: 10.1007/978-3-031-06833-1Online resources:

Summary: Introduction -- Review of Mathematical Concepts -- Topological Quantum Codes -- Color Codes -- The Interplay between Color Codes and Toric Codes.Summary: 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.PPN: PPN: 1813786976Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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