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Quantum Codes for Topological Quantum Computation

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kr 117

Quantum Codes for Topological Quantum Computation

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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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.
Produktdetaljer
Sprog: Engelsk
Sider: 116
ISBN-13: 9783031068324
Indbinding: Paperback
Udgave:
ISBN-10: 3031068327
Udg. Dato: 5 aug 2022
Længde: 10mm
Bredde: 155mm
Højde: 234mm
Forlag: Springer International Publishing AG
Oplagsdato: 5 aug 2022
Forfatter(e) Waldir Silva Soares Jr., Eduardo Brandani da Silva, Clarice Dias de Albuquerque


Kategori Kodeteori og kryptologi


Sprog Engelsk


Indbinding Paperback


Sider 116


Udgave


Længde 10mm


Bredde 155mm


Højde 234mm


Udg. Dato 5 aug 2022


Oplagsdato 5 aug 2022

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