**CBMS Regional Conference Series in Mathematics**

Volume: 112;
2010;
115 pp;
Softcover

MSC: Primary 57; 81; 68; 18;

Print ISBN: 978-0-8218-4930-9

Product Code: CBMS/112

List Price: $36.00

Individual Price: $28.80

**Electronic ISBN: 978-1-4704-1570-9
Product Code: CBMS/112.E**

List Price: $36.00

Individual Member Price: $28.80

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#### Supplemental Materials

# Topological Quantum Computation

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*Zhenghan Wang*

A co-publication of the AMS and CBMS

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.

#### Table of Contents

# Table of Contents

## Topological Quantum Computation

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- Acknowledgments xiii14 free
- Temperley-Lieb-Jones theories 116 free
- Quantum circuit model 2540
- Approximation of the Jones polynomial 3550
- Ribbon fusion categories 4156
- (2+1)-TQFTs 5772
- TQFTs in nature 7388
- Topological quantum computers 89104
- Topological phases of matter 97112
- Outlook and open problems 109124
- Bibliography 111126
- Back Cover Back Cover1134

#### Readership

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