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Topological Quantum Computation

Zhenghan Wang Microsoft, Santa Barbara, CA
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-4930-9
Product Code: CBMS/112
List Price: $39.00 Individual Price:$31.20
Electronic ISBN: 978-1-4704-1570-9
Product Code: CBMS/112.E
List Price: $36.00 MAA Member Price:$32.40
AMS Member Price: $28.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$58.50
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Topological Quantum Computation
Zhenghan Wang Microsoft, Santa Barbara, CA
A co-publication of the AMS and CBMS
Available Formats:
 Softcover ISBN: 978-0-8218-4930-9 Product Code: CBMS/112
 List Price: $39.00 Individual Price:$31.20
 Electronic ISBN: 978-1-4704-1570-9 Product Code: CBMS/112.E
 List Price: $36.00 MAA Member Price:$32.40 AMS Member Price: $28.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$58.50
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1122010; 115 pp
MSC: Primary 57; 81; 68; 18;

Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators.

This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.

A co-publication of the AMS and CBMS.

Graduate students and research mathematicians interested in quantum computers, topological quantum field theory.

• Chapters
• Chapter 1. Temperley-Lieb-Jones theories
• Chapter 2. Quantum circuit model
• Chapter 3. Approximation of the Jones polynomial
• Chapter 4. Ribbon fusion categories
• Chapter 5. (2+1)-TQFTs
• Chapter 6. TQFTs in nature
• Chapter 7. Topological quantum computers
• Chapter 8. Topological phases of matter
• Chapter 9. Outlook and open problems

• Request Review Copy
Volume: 1122010; 115 pp
MSC: Primary 57; 81; 68; 18;

Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators.

This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.

A co-publication of the AMS and CBMS.

Graduate students and research mathematicians interested in quantum computers, topological quantum field theory.

• Chapters
• Chapter 1. Temperley-Lieb-Jones theories
• Chapter 2. Quantum circuit model
• Chapter 3. Approximation of the Jones polynomial
• Chapter 4. Ribbon fusion categories
• Chapter 5. (2+1)-TQFTs
• Chapter 6. TQFTs in nature
• Chapter 7. Topological quantum computers
• Chapter 8. Topological phases of matter
• Chapter 9. Outlook and open problems
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