Quantum Computing for Programmers

375 Pages·2022·3.544 MB·English

by  Robert Hundt

QuantumComputingforProgrammers
Thisintroductiontoquantumcomputingfromaclassicalprogrammer’sperspectiveis
meantforstudentsandpractitionersalike.Morethan25fundamentalalgorithmsare
explainedwithfullmathematicalderivationsandclassicalcodeforsimulation,using
anopen-sourcecodebasedevelopedfromthegroundupinPythonandC++.
After presenting the basics of quantum computing, the author focuses on algo-
rithms and the infrastructure to simulate them efficiently, beginning with quantum
teleportation,superdensecoding,Bernstein–Vazirani’salgorithm,andDeutsc–Jozsa’s
algorithm.Coverageofadvancedalgorithmsincludesthequantumsupremacyexperi-
ment,quantumFouriertransform,phaseestimation,Shor’salgorithm,Grover’salgo-
rithm with quantum counting and amplitude amplification, quantum random walks,
and the Solovay–Kitaev algorithm for gate approximation. Quantum simulation is
explored with the variational quantum eigensolver, quantum approximate optimiza-
tion,andtheNP-completeMax-CutandSubset-Sumalgorithms.
The book also discusses issues around programmer productivity, quantum noise,
errorcorrection,andchallengesforquantumprogramminglanguages,compilers,and
tools,withafinalsectiononcompilertechniquesfortranspilation.
RobertHundtisaDistinguishedEngineeratGoogle,whereheledsoftwaredevelop-
mentforGoogle’sTPUsupercomputers,theXLAcompilerforTensorFlow,anopen-
source CUDA compiler, and currently the high-level synthesis toolchain XLS. He
has more than 25 scientific publications, holds more than 35 patents, and is a senior
memberofIEEE.

Quantum Computing for
Programmers
ROBERT HUNDT
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781009098175
DOI:10.1017/9781009099974
©RobertHundt2022
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andtotheprovisionsofrelevantcollectivelicensingagreements,
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Firstpublished2022
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LibraryofCongressCataloging-in-PublicationData
Names:Hundt,Robert,author.
Title:Quantumcomputingforprogrammers/RobertHundt.
Description:Cambridge,UnitedKingdom;NewYork,NY:Cambridge
UniversityPress,2022.|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2021044761(print)|LCCN2021044762(ebook)|
ISBN9781009098175(hardback)|ISBN9781009099974(epub)
Subjects:LCSH:Quantumcomputing.|BISAC:COMPUTERS/General
Classification:LCCQA76.889.H862022(print)|LCCQA76.889(ebook)|
DDC006.3/843–dc23/eng/20211105
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ToMary,Thalia,andJohannes

Contents
Acknowledgments pagex
Introduction xi
1 TheMathematicalMinimum 1
1.1 ComplexNumbers 1
1.2 DiracNotation,Bras,andKets 2
1.3 TensorProduct 5
1.4 UnitaryandHermitianMatrices 6
1.5 HermitianAdjointofExpressions 6
1.6 EigenvaluesandEigenvectors 7
1.7 TraceofaMatrix 8
2 QuantumComputingFundamentals 9
2.1 Tensors 9
2.2 Qubits 13
2.3 States 15
2.4 HelperFunctions 24
2.5 Operators 25
2.6 Single-QubitGates 33
2.7 ControlledGates 46
2.8 QuantumCircuitNotation 51
2.9 BlochSphere 55
2.10 GlobalPhase 59
2.11 Entanglement 60
2.12 No-CloningTheorem 65
2.13 Uncomputation 66
2.14 ReducedDensityMatrixandPartialTrace 68
2.15 Measurement 72
3 SimpleAlgorithms 78
3.1 RandomNumberGenerator 78
3.2 GateEquivalences 79
3.3 ClassicalArithmetic 89
3.4 SwapTest 93
viii Contents
3.5 QuantumTeleportation 97
3.6 SuperdenseCoding 102
3.7 Bernstein–VaziraniAlgorithm 105
3.8 Deutsch’sAlgorithm 108
3.9 Deutsch–JozsaAlgorithm 118
4 Scalable,FastSimulation 122
4.1 SimulationComplexity 122
4.2 QuantumRegisters 124
4.3 Circuits 126
4.4 FastGateApplication 134
4.5 AcceleratedGateApplication 139
4.6 SparseRepresentation 145
5 BeyondClassical 149
5.1 10,000Years,2Days,or200Seconds 150
5.2 QuantumRandomCircuitAlgorithm 150
5.3 CircuitConstruction 152
5.4 Estimation 155
5.5 Evaluation 158
6 ComplexAlgorithms 160
6.1 PhaseKick 161
6.2 QuantumFourierTransform 163
6.3 QuantumArithmetic 172
6.4 PhaseEstimation 180
6.5 Shor’sAlgorithm 189
6.6 OrderFinding 196
6.7 Grover’sAlgorithm 210
6.8 AmplitudeAmplification 227
6.9 QuantumCounting 230
6.10 QuantumRandomWalk 234
6.11 VariationalQuantumEigensolver 240
6.12 QuantumApproximateOptimizationAlgorithm 253
6.13 MaximumCutAlgorithm 254
6.14 SubsetSumAlgorithm 262
6.15 Solovay–KitaevTheoremandAlgorithm 266
7 QuantumErrorCorrection 278
7.1 QuantumNoise 278
7.2 QuantumErrorCorrection 284
7.3 Nine-QubitShorCode 289
Contents ix
8 QuantumLanguages,Compilers,andTools 292
8.1 ChallengesforQuantumCompilation 293
8.2 QuantumProgrammingModel 294
8.3 QuantumProgrammingLanguages 294
8.4 CompilerOptimization 303
8.5 Transpilation 311
Appendix: SparseImplementation 322
References 335
Index 343