Quantum Computing Devices: Principles, Designs, and Analysis (Chapman & Hall Crc Applied Mathematics and Nonlinear Science Series)

565 Pages·2006·4.28 MB·English

by  Goong Chen

CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
QUANTUM COMPUTING DEVICES
P , D , A
RINCIPLES ESIGNS AND NALYSIS
CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
Series Editors Goong Chen andThomas J. Bridges CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
QUANTUM COMPUTING DEVICES
Published Titles
Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications,
Victor A. Galaktionov
Introduction to Fuzzy Systems, Guanrong Chen and Trung Tat Pham P , D , A
Introduction to Partial Differential Equations with MATLAB®,Matthew P. Coleman RINCIPLES ESIGNS AND NALYSIS
Mathematical Methods in Physics and Engineering with Mathematica,
Ferdinand F. Cap
Optimal Estimation of Dynamic Systems, John L. Crassidis and John L. Junkins
Quantum Computing Devices: Principles, Designs, and Analysis, Goong Chen,
David A. Church, Berthold-Georg Englert, Carsten Henkel, Bernd Rohwedder,
Marlan O. Scully, and M. Suhail Zubairy
Forthcoming Titles
Mathematical Theory of Quantum Computation, Goong Chen and Zijian Diao Goong Chen
Stochastic Partial Differential Equations, Pao-Liu Chow
David A. Church
Berthold-Georg Englert
Carsten Henkel
Bernd Rohwedder
Marlan O. Scully
M. Suhail Zubairy
Boca Raton London New York
Chapman & Hall/CRC is an imprint of the
Taylor & Francis Group, an informa business
CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
Series Editors Goong Chen andThomas J. Bridges CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
QUANTUM COMPUTING DEVICES
Published Titles
Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications,
Victor A. Galaktionov
Introduction to Fuzzy Systems, Guanrong Chen and Trung Tat Pham P , D , A
Introduction to Partial Differential Equations with MATLAB®,Matthew P. Coleman RINCIPLES ESIGNS AND NALYSIS
Mathematical Methods in Physics and Engineering with Mathematica,
Ferdinand F. Cap
Optimal Estimation of Dynamic Systems, John L. Crassidis and John L. Junkins
Quantum Computing Devices: Principles, Designs, and Analysis, Goong Chen,
David A. Church, Berthold-Georg Englert, Carsten Henkel, Bernd Rohwedder,
Marlan O. Scully, and M. Suhail Zubairy
Forthcoming Titles
Mathematical Theory of Quantum Computation, Goong Chen and Zijian Diao Goong Chen
Stochastic Partial Differential Equations, Pao-Liu Chow
David A. Church
Berthold-Georg Englert
Carsten Henkel
Bernd Rohwedder
Marlan O. Scully
M. Suhail Zubairy
Boca Raton London New York
Chapman & Hall/CRC is an imprint of the
Taylor & Francis Group, an informa business
Chapman & Hall/CRC
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Library of Congress Cataloging‑in‑Publication Data
Quantum computing devices : principles, designs, and analysis / Goong Chen …
[et al.].
p. cm. ‑‑ (Chapman & Hall/CRC applied mathematics and nonlinear
science series ; #6)
Includes bibliographical references and index.
ISBN 1‑58488‑681‑1 (alk. paper)
1. Quantum computers. I. Chen, Goong, 1950‑ II. Title. III. Series.
QA76.889.Q832 2006
004.1‑‑dc22 2006049559
Visit the Taylor & Francis Web site at
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and the CRC Press Web site at
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GoongChen
DepartmentofMathematicsandInstituteforQuantumStudies
TexasA&MUniversity
CollegeStation,TX77843,U.S.A.
DavidA.Church
DepartmentofPhysics
TexasA&MUniversity
CollegeStation,TX77843,U.S.A.
Berthold-GeorgEnglert
DepartmentofPhysics
NationalUniversityofSingapore
Singapore
CarstenHenkel
InstitutfürPhysik,UniversitätPotsdam
D-14469Potsdam,Germany
BerndRohwedder
InstitutodeFísica
UniversidadeFederaldoRiodeJaneiro
Cx.P.68528,CEP21941-972
RiodeJaneiro,Brazil
MarlanO.Scully
DepartmentsofPhysics,andElectricalandChemicalEngineering
andInstituteforQuantumStudies
TexasA&MUniversity
CollegeStation,TX77843,U.S.A.
and
DepartmentsofChemistry,andMechanicalandAerospaceEngineering
PrincetonUniversity
Princeton,NJ08544,U.S.A.
and
Max-PlanckInstitutfürQuantenoptik
D-85748Garching,Germany
M.SuhailZubairy
DepartmentofPhysicsandInstituteforQuantumStudies
TexasA&MUniversity
CollegeStation,TX77843,U.S.A.

To Professor and Mrs. Pah (Paul) I. and May T. Chen
(cid:6392)(cid:4079)(cid:3755)(cid:1796)(cid:5082)(cid:3474)(cid:3460)(cid:1431)(cid:1435)(cid:1331)(cid:1830)(cid:2733)(cid:3900)

Contents
Preface xv
1 Foundations of Quantum Informatics: Spins, the EPR Prob-
lem,andLandauer’sPrinciple 1
1.1 Spins: TheStern–Gerlachexperimentandspinfilter . . . . . 2
1.2 EPRandBell’sinequalities . . . . . . . . . . . . . . . . . . . . 7
1.2.1 TheEPRproblem . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 ResolvingtheEPRconundrum . . . . . . . . . . . . . . 10
1.2.3 Bell’sinequality . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 TheLandauerprinciple. . . . . . . . . . . . . . . . . . . . . . . 17
2 QuantumComputationandQuantumSystems 27
2.1 Introduction: Turingmachinesandbinarylogicgates . . . . . 27
2.2 Quantummechanicalsystems;basicsofatomsandmolecules 33
2.2.1 Quantumprobability . . . . . . . . . . . . . . . . . . . . 33
2.2.2 Basicsofatomsandmolecules. . . . . . . . . . . . . . . 36
2.3 Hilbertspaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4 ComplexfinitedimensionalHilbertspacesandtensorproducts 48
2.5 QuantumTuringmachines . . . . . . . . . . . . . . . . . . . . 49
2.6 Universalityofelementaryquantumgates;quantumcircuits 50
2.7 Quantumalgorithms . . . . . . . . . . . . . . . . . . . . . . . . 60
2.7.1 TheDeutsch–Jozsaproblem . . . . . . . . . . . . . . . . 60
2.7.2 TheBernstein–Vaziraniproblem . . . . . . . . . . . . . 62
2.7.3 Simon’sproblem . . . . . . . . . . . . . . . . . . . . . . . 64
2.7.4 Grover’squantumsearchalgorithm . . . . . . . . . . . 65
2.7.5 Shor’sfactorizationalgorithm . . . . . . . . . . . . . . . 73
2.8 Quantumadderandmultiplier . . . . . . . . . . . . . . . . . . 75
2.9 Quantumerrorcorrectioncodes . . . . . . . . . . . . . . . . . . 79
2.10 Lasers: aheuristicintroduction . . . . . . . . . . . . . . . . . . 88
2.11 Quantumcomputingdevicesandrequirements . . . . . . . . . 91
3 Two-LevelAtomsandCavityQED 101
3.1 Two-levelatoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.1.1 Atom–lightinteraction . . . . . . . . . . . . . . . . . . . 103
ix