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Quantum Codes for Topological Quantum Computation : Mathematics and Statistics (R0) - Clarice Dias de Albuquerque

Quantum Codes for Topological Quantum Computation

By: Clarice Dias de Albuquerque, Eduardo Brandani da Silva da, Waldir Silva Soares Jr.

eText | 4 August 2022

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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.

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Non-FictionSciencePhysicsQuantum Physics & Quantum Mechanics & Quantum Field TheoryComputing & I.T.Computer ScienceMathematical Theory of ComputationReference, Information & Interdisciplinary SubjectsResearch & InformationCoding Theory & CryptologyMathematicsLibrary & Info Sciences
Library & Information ServicesInformation theory

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