Quantum Computing for Computer Scientists

402 Pages·2008·2.51 MB·English

by  Noson S. Yanofsky, Mirco A. Mannucci

book-yanofsky CUUS235-Yanofsky ISBN 9780521879965 June 6, 2008 16:17 Char Count= 0
Quantum Computing for Computer Scientists
The multidisciplinary field of quantum computing strives to exploit some
of the uncanny aspects of quantum mechanics to expand our computa-
tional horizons. Quantum Computing for Computer Scientists takes read-
ers on a tour of this fascinating area of cutting-edge research. Written
in an accessible yet rigorous fashion, this book employs ideas and tech-
niques familiar to every student of computer science. The reader is not
expected to have any advanced mathematics or physics background. Af-
ter presenting the necessary prerequisites, the material is organized to
look at different aspects of quantum computing from the specific stand-
point of computer science. There are chapters on computer architecture,
algorithms, programming languages, theoretical computer science, cryp-
tography, information theory, and hardware. The text has step-by-step
examples, more than two hundred exercises with solutions, and program-
ming drills that bring the ideas of quantum computing alive for today’s
computer science students and researchers.
Noson S. Yanofsky, PhD, is an Associate Professor in the Department
of Computer and Information Science at Brooklyn College, City Univer-
sity of New York and at the PhD Program in Computer Science at The
Graduate Center of CUNY.
Mirco A. Mannucci, PhD, is the founder and CEO of HoloMathics, LLC,
a research and development company with a focus on innovative mathe-
matical modeling. He also serves as Adjunct Professor of Computer Sci-
ence at George Mason University and the University of Maryland.
i
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QUANTUM COMPUTING FOR
COMPUTER SCIENTISTS
Noson S. Yanofsky
Brooklyn College, City University of New York
and
Mirco A. Mannucci
HoloMathics, LLC
iii
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cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sa˜o Paulo, Delhi
Cambridge University Press
32 Avenue of the Americas, New York, NY 10013-2473, USA
www.cambridge.org
Information on this title: www.cambridge.org/9780521879965
⃝C Noson S. Yanofsky and Mirco A. Mannucci 2008
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 2008
Printed in the United States of America
A catalog record for this publication is available from the British Library.
Library of Congress Cataloging in Publication data
Yanofsky, Noson S., 1967–
Quantum computing for computer scientists / Noson S. Yanofsky and
Mirco A. Mannucci.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-521-87996-5 (hardback)
1. Quantum computers. I. Mannucci, Mirco A., 1960– II. Title.
QA76.889.Y35 2008
004.1–dc22 2008020507
ISBN 978-0-521-879965 hardback
Cambridge University Press has no responsibility for
the persistence or accuracy of URLs for external or
third-party Internet Web sites referred to in this publication
and does not guarantee that any content on such
Web sites is, or will remain, accurate or appropriate.
iv
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Dedicated to
Moishe and Sharon Yanofsky
and
to the memory of
Luigi and Antonietta Mannucci
v
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Wisdom is one thing: to know the thought by which
all things are directed through all things.
˜
Heraclitus of Ephesus (535–475 BCE)
as quoted in Diogenes Laertius’s
Lives and Opinions of Eminent Philosophers
Book IX, 1.
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Contents
Preface xi
1 Complex Numbers 7
1.1 Basic Definitions 8
1.2 The Algebra of Complex Numbers 10
1.3 The Geometry of Complex Numbers 15
2 Complex Vector Spaces 29
n
2.1 C as the Primary Example 30
2.2 Definitions, Properties, and Examples 34
2.3 Basis and Dimension 45
2.4 Inner Products and Hilbert Spaces 53
2.5 Eigenvalues and Eigenvectors 60
2.6 Hermitian and Unitary Matrices 62
2.7 Tensor Product of Vector Spaces 66
3 The Leap from Classical to Quantum 74
3.1 Classical Deterministic Systems 74
3.2 Probabilistic Systems 79
3.3 Quantum Systems 88
3.4 Assembling Systems 97
4 Basic Quantum Theory 103
4.1 Quantum States 103
4.2 Observables 115
4.3 Measuring 126
4.4 Dynamics 129
4.5 Assembling Quantum Systems 132
5 Architecture 138
5.1 Bits and Qubits 138
vii
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viii Contents
5.2 Classical Gates 144
5.3 Reversible Gates 151
5.4 Quantum Gates 158
6 Algorithms 170
6.1 Deutsch’s Algorithm 171
6.2 The Deutsch–Jozsa Algorithm 179
6.3 Simon’s Periodicity Algorithm 187
6.4 Grover’s Search Algorithm 195
6.5 Shor’s Factoring Algorithm 204
7 Programming Languages 220
7.1 Programming in a Quantum World 220
7.2 Quantum Assembly Programming 221
7.3 Toward Higher-Level Quantum Programming 230
7.4 Quantum Computation Before Quantum Computers 237
8 Theoretical Computer Science 239
8.1 Deterministic and Nondeterministic Computations 239
8.2 Probabilistic Computations 246
8.3 Quantum Computations 251
9 Cryptography 262
9.1 Classical Cryptography 262
9.2 Quantum Key Exchange I: The BB84 Protocol 268
9.3 Quantum Key Exchange II: The B92 Protocol 273
9.4 Quantum Key Exchange III: The EPR Protocol 275
9.5 Quantum Teleportation 277
10 Information Theory 284
10.1 Classical Information and Shannon Entropy 284
10.2 Quantum Information and von Neumann Entropy 288
10.3 Classical and Quantum Data Compression 295
10.4 Error-Correcting Codes 302
11 Hardware 305
11.1 Quantum Hardware: Goals and Challenges 306
11.2 Implementing a Quantum Computer I: Ion Traps 311
11.3 Implementing a Quantum Computer II: Linear Optics 313
11.4 Implementing a Quantum Computer III: NMR
and Superconductors 315
11.5 Future of Quantum Ware 316
Appendix A Historical Bibliography of Quantum Computing 319
by Jill Cirasella
A.1 Reading Scientific Articles 319
A.2 Models of Computation 320