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OverviewThis 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. Full Product DetailsAuthor: Clarice Dias de Albuquerque , Eduardo Brandani da Silva , Waldir Silva Soares Jr.Publisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2022 Weight: 0.203kg ISBN: 9783031068324ISBN 10: 3031068327 Pages: 116 Publication Date: 05 August 2022 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents[preliminary]1 An Overview on Quantum Codes1.1 Previous Results1.2 Goals1.3 Some Classes of Quantum Error-Correcting Codes1.4 Quantum Error-Correcting Codes1.4.1 Formalism of Stabilizer Codes1.5 Topological Quantum Codes1.5.1 Topological Stabilizer Codes1.6 CSS Codes1.7 Surface Codes1.8 Toric Quantum Code, g = 11.9 Hyperbolic Surface Codes, g ≥ 21.10 Color Codes 2 Preliminaries2.1 Upper Half-Plane Model2.2 Unit Open Disc Model2.3 Geometrical Properties in H2 and [Delta]2.4 Tessellations in Euclidean and Hyperbolic Planes 3 Surface Codes 293.1 Toric Codes, g = 13.2 Projective Plane Codes, g = 03.3 Homological Quantum Codes, g = 13.4 g-Toric Codes, g ≥ 2 4 Color Codes4.1 Quantum Color Codes4.2 Hyperbolic Color Codes4.3 Polygonal Color CodesReviewsAuthor InformationClarice 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. Tab Content 6Author Website:Countries AvailableAll regions |
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