Softcover ISBN:  9780821849309 
Product Code:  CBMS/112 
List Price:  $41.00 
Individual Price:  $32.80 
eBook ISBN:  9781470415709 
Product Code:  CBMS/112.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $30.40 
Softcover ISBN:  9780821849309 
eBook: ISBN:  9781470415709 
Product Code:  CBMS/112.B 
List Price:  $79.00$60.00 
Softcover ISBN:  9780821849309 
Product Code:  CBMS/112 
List Price:  $41.00 
Individual Price:  $32.80 
eBook ISBN:  9781470415709 
Product Code:  CBMS/112.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $30.40 
Softcover ISBN:  9780821849309 
eBook ISBN:  9781470415709 
Product Code:  CBMS/112.B 
List Price:  $79.00$60.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 112; 2010; 115 ppMSC: 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 manyanyon systems and processed by braiding nonabelian 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 errorminimizing hypothetical hardware: topological phases of matter are faultavoiding 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: TemperleyLiebJones 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 copublication of the AMS and CBMS.
ReadershipGraduate students and research mathematicians interested in quantum computers, topological quantum field theory.

Table of Contents

Chapters

Chapter 1. TemperleyLiebJones 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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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 manyanyon systems and processed by braiding nonabelian 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 errorminimizing hypothetical hardware: topological phases of matter are faultavoiding 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: TemperleyLiebJones 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 copublication of the AMS and CBMS.
Graduate students and research mathematicians interested in quantum computers, topological quantum field theory.

Chapters

Chapter 1. TemperleyLiebJones 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