Quantum Computing for Computer Scientists

402 Pages·2008·2.51 MB·English

by  Noson S. Yanofsky

book-yanofsky CUUS235-Yanofsky ISBN9780521879965 June6,2008 16:17 CharCount=0
Quantum Computing for Computer Scientists
Themultidisciplinaryfieldofquantumcomputingstrivestoexploitsome
of the uncanny aspects of quantum mechanics to expand our computa-
tionalhorizons.QuantumComputingforComputerScientiststakesread-
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
expectedtohaveanyadvancedmathematicsorphysicsbackground.Af-
ter presenting the necessary prerequisites, the material is organized to
look at different aspects of quantum computing from the specific stand-
pointofcomputerscience.Therearechaptersoncomputerarchitecture,
algorithms,programminglanguages,theoreticalcomputerscience,cryp-
tography, information theory, and hardware. The text has step-by-step
examples,morethantwohundredexerciseswithsolutions,andprogram-
ming drills that bring the ideas of quantum computing alive for today’s
computersciencestudentsandresearchers.
Noson S. Yanofsky, PhD, is an Associate Professor in the Department
ofComputerandInformationScienceatBrooklynCollege,CityUniver-
sity of New York and at the PhD Program in Computer Science at The
GraduateCenterofCUNY.
MircoA.Mannucci,PhD,isthefounderandCEOofHoloMathics,LLC,
aresearchanddevelopmentcompanywithafocusoninnovativemathe-
maticalmodeling.HealsoservesasAdjunctProfessorofComputerSci-
enceatGeorgeMasonUniversityandtheUniversityofMaryland.
i

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QUANTUM COMPUTING FOR
COMPUTER SCIENTISTS
Noson S. Yanofsky
BrooklynCollege,CityUniversityofNewYork
and
Mirco A. Mannucci
HoloMathics,LLC
iii
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cambridgeuniversitypress
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CambridgeUniversityPress
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521879965
(cid:1)C NosonS.YanofskyandMircoA.Mannucci2008
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithout
thewrittenpermissionofCambridgeUniversityPress.
Firstpublished2008
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationdata
Yanofsky,NosonS.,1967–
Quantumcomputingforcomputerscientists/NosonS.Yanofskyand
MircoA.Mannucci.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN 978-0-521-87996-5(hardback)
1.Quantumcomputers. I.Mannucci,MircoA.,1960– II.Title.
QA76.889.Y35 2008
004.1–dc22 2008020507
ISBN 978-0-521-879965hardback
CambridgeUniversityPresshasnoresponsibilityfor
thepersistenceoraccuracyofURLsforexternalor
third-partyInternetWebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuch
Websitesis,orwillremain,accurateorappropriate.
iv
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Dedicatedto
MoisheandSharonYanofsky
and
tothememoryof
LuigiandAntoniettaMannucci
v
book-yanofsky CUUS235-Yanofsky ISBN9780521879965 June6,2008 16:17 CharCount=0
Wisdomisonething:toknowthethoughtbywhich
allthingsaredirectedthroughallthings.
˜
HeraclitusofEphesus(535–475BCE)
asquotedinDiogenesLaertius’s
LivesandOpinionsofEminentPhilosophers
BookIX,1.
vi
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Contents
Preface xi
1 Complex Numbers 7
1.1 BasicDefinitions 8
1.2 TheAlgebraofComplexNumbers 10
1.3 TheGeometryofComplexNumbers 15
2 Complex Vector Spaces 29
2.1 Cnas the Primary Example 30
2.2 Definitions,Properties,andExamples 34
2.3 BasisandDimension 45
2.4 InnerProductsandHilbertSpaces 53
2.5 EigenvaluesandEigenvectors 60
2.6 HermitianandUnitaryMatrices 62
2.7 TensorProductofVectorSpaces 66
3 The Leap from Classical to Quantum 74
3.1 ClassicalDeterministicSystems 74
3.2 ProbabilisticSystems 79
3.3 QuantumSystems 88
3.4 AssemblingSystems 97
4 Basic Quantum Theory 103
4.1 QuantumStates 103
4.2 Observables 115
4.3 Measuring 126
4.4 Dynamics 129
4.5 AssemblingQuantumSystems 132
5 Architecture 138
5.1 BitsandQubits 138
vii
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viii Contents
5.2 ClassicalGates 144
5.3 ReversibleGates 151
5.4 QuantumGates 158
6 Algorithms 170
6.1 Deutsch’sAlgorithm 171
6.2 TheDeutsch–JozsaAlgorithm 179
6.3 Simon’sPeriodicityAlgorithm 187
6.4 Grover’sSearchAlgorithm 195
6.5 Shor’sFactoringAlgorithm 204
7 Programming Languages 220
7.1 ProgramminginaQuantumWorld 220
7.2 QuantumAssemblyProgramming 221
7.3 TowardHigher-LevelQuantumProgramming 230
7.4 QuantumComputationBeforeQuantumComputers 237
8 Theoretical Computer Science 239
8.1 DeterministicandNondeterministicComputations 239
8.2 ProbabilisticComputations 246
8.3 QuantumComputations 251
9 Cryptography 262
9.1 ClassicalCryptography 262
9.2 QuantumKeyExchangeI:TheBB84Protocol 268
9.3 QuantumKeyExchangeII:TheB92Protocol 273
9.4 QuantumKeyExchangeIII:TheEPRProtocol 275
9.5 QuantumTeleportation 277
10 Information Theory 284
10.1 ClassicalInformationandShannonEntropy 284
10.2 QuantumInformationandvonNeumannEntropy 288
10.3 ClassicalandQuantumDataCompression 295
10.4 Error-CorrectingCodes 302
11 Hardware 305
11.1 QuantumHardware:GoalsandChallenges 306
11.2 ImplementingaQuantumComputerI:IonTraps 311
11.3 ImplementingaQuantumComputerII:LinearOptics 313
11.4 ImplementingaQuantumComputerIII:NMR
andSuperconductors 315
11.5 FutureofQuantumWare 316
Appendix A Historical Bibliography of Quantum Computing 319
byJillCirasella
A.1 ReadingScientificArticles 319
A.2 ModelsofComputation 320