Overview
- 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
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (5 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Quantum Codes for Topological Quantum Computation
Authors: Clarice Dias de Albuquerque, Eduardo Brandani da Silva, Waldir Silva Soares Jr.
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-031-06833-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-06832-4Published: 05 August 2022
eBook ISBN: 978-3-031-06833-1Published: 04 August 2022
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: VIII, 116
Number of Illustrations: 11 b/w illustrations, 19 illustrations in colour