Quantum Computing
The twentieth century witnessed the birth of revolutionary ideas in the phys ical sciences. These ideas began to shake the traditional view of the universe dating back to the days of Newton, even to the days of Galileo. Albert Ein stein is usually ident
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Advisory Board: S. Amari G. Brassard M. Conrad K.A. De Jong C.C.A.M. Gielen T. Head 1. Kari 1. Landweber T. Martinetz Z. Michalewicz M.C. Mozer E.Oja J. Reif H. Rubin A. Salomaa M. Schoenauer H.-P. Schwefel D. Whitley E. Winfree J.M. Zurada
Springer-Verlag Berlin Heidelberg GmbH
Mika Hirvensalo
Quantum Computing With 5 Figures
Springer
Author Mika Hirvensalo Department of Mathematics University of Turku 20014 Turku, Finland [email protected]
Series Editors G. Rozenberg (Managing Editor) Th. Băck, A.E. Eiben, J.N. Kok, H.P. Spaink Leiden Center for Natural Computing Leiden University Niels Bohrweg 1 2333 CA Leiden, The Netherlands [email protected]
Library of Congress Cataloging-in-Publication Data Quantum computing p.cm. ISBN 978-3-662-04463-6 ISBN 978-3-662-04461-2 (eBook) DOI 10.1007/978-3-662-04461-2 1. Quantum computers. QA76.889.Q82 2001 2001020738 004.1--dc21
ACM Computing Classification ( 1998 ): F.l-2, G .1.2, G .3, H.l.l, 1.1.2, J.2 ISBN 978-3-662-04463-6 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of th1s publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. http://www.springer.de © Springer-Verlag Berlin Heidelberg 2001
Originally published by Springer-Verlag Berlin Heidelberg New York in 2001 Softcover reprint ofthe hardcover lst edition 2001 The use of general descriptive names, trademarks, 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. Cover Design: KiinkelLopka, Heidelberg Typesetting: Camera ready by the author Printed on acid-free paper SPIN 10723406
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Preface
The twentieth century witnessed the birth of revolutionary ideas in the physical sciences. These ideas began to shake the traditional view of the universe dating back to the days of Newton, even to the days of Galileo. Albert Einstein is usually identified as the creator of the relativity theory, a theory that is used to model the behavior of the huge macrosystems of astronomy. Another new view of the physical world was supplied by quantum physics, which turned out to be successful in describing phenomena in the microworld, the behavior of particles of atomic size. Even though the first ideas of automatic information processing are quite old, I feel justified in saying that the twentieth century also witnessed the birth of computer science. As a mathematician, by the term "computer science", I mean the more theoretical parts of this vast res
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