Quantum Computation with Topological Codes From Qubit to Topological
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topolog
- PDF / 7,246,569 Bytes
- 148 Pages / 439.37 x 666.142 pts Page_size
- 11 Downloads / 202 Views
Keisuke Fujii
Quantum Computation with Topological Codes From Qubit to Topological Fault-Tolerance 123
SpringerBriefs in Mathematical Physics Volume 8
Series editors Nathanaël Berestycki, Cambridge, UK Mihalis Dafermos, Cambridge, UK Tohru Eguchi, Tokyo, Japan Atsuo Kuniba, Tokyo, Japan Matilde Marcolli, Pasadena, USA Bruno Nachtergaele, Davis, USA
More information about this series at http://www.springer.com/series/11953
Keisuke Fujii
Quantum Computation with Topological Codes From Qubit to Topological Fault-Tolerance
123
Keisuke Fujii Graduate School of Science Kyoto University Kyoto Japan
ISSN 2197-1757 ISSN 2197-1765 (electronic) SpringerBriefs in Mathematical Physics ISBN 978-981-287-995-0 ISBN 978-981-287-996-7 (eBook) DOI 10.1007/978-981-287-996-7 Library of Congress Control Number: 2015952538 Springer Singapore Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Science+Business Media Singapore Pte Ltd. is part of Springer Science+Business Media (www.springer.com)
Preface
In 1982, Richard Feynman pointed out that a simulation of quantum systems on classical computers is generally inefficient because the dimension of the state space increases exponentially with the number of particles [1]. Instead, quantum systems could be simulated efficiently by other quantum systems. David Deutsch put this idea forward by formulating a quantum version of a Turing machine [2]. Quantum computation enables us to solve certain kinds of problems that are thought to be intractable with classical computers such as the prime factoring problem and an approximation of the Jones polynomial. It has a great possibility to disprove the extended (strong) Church–Turing thesis, i.e., that any computational process on realistic devices can be simulated efficiently on a probabilistic Turing machine. However, for this statement to make sense, we need to determine whether or not quantum computation is a
Data Loading...
