Topological Quantum Computation

by Zhenghan Wang

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 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 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.

Genres: Physics, Computer Science

115 pages, Paperback

First published May 29, 2010

Reviews

[Kevin K. Gillette · Rating 5 out of 5]

Simply fascinating! This is an exhilirating area of research that lives at the crossrods of theoretical and applied physics, computer science, and algebraic graph theory. Dr. Wang provides an engaging and well-developed summary of the research avenues that feed into this topic, and brings them all together later in the book, having provided sufficient motivation for all the components. Well-written and self-contained, this book is appropriate for any researcher in quantum computation and anyone with strong mathematical maturity who wishes to explore this field for the first time.