Quantum Computing for Computer Architects (Synthesis Lectures on Computer Architecture)

203 Pages·2011·1.9 MB·English

by  Tzvetan Metodi

Quantum Computing
for Computer Architects
SecondEdition
Synthesis Lectures on Computer
Architecture
Editor
MarkD.Hill,UniversityofWisconsin
SynthesisLecturesonComputerArchitecturepublishes50-to100-pagepublicationsontopics
pertainingtothescienceandartofdesigning,analyzing,selectingandinterconnectinghardware
componentstocreatecomputersthatmeetfunctional,performanceandcostgoals.Thescopewill
largelyfollowthepurviewofpremiercomputerarchitectureconferences,suchasISCA,HPCA,
MICRO,andASPLOS.
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QuantumComputingforComputerArchitects,SecondEdition
TzvetanS.Metodi,ArvinI.Faruque,andFredericT.Chong
www.morganclaypool.com
ISBN:9781608456192 paperback
ISBN:9781608456208 ebook
DOI10.2200/S00331ED1V01Y201101CAC013
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONCOMPUTERARCHITECTURE
Lecture#13
SeriesEditor:MarkD.Hill,UniversityofWisconsin
SeriesISSN
SynthesisLecturesonComputerArchitecture
Print1935-3235 Electronic1935-3243
Quantum Computing
for Computer Architects
SecondEdition
Tzvetan S.Metodi
TheAerospaceCorporation
Arvin I.Faruque
UniversityofCalifornia,SantaBarbara
FredericT.Chong
UniversityofCalifornia,SantaBarbara
SYNTHESISLECTURESONCOMPUTERARCHITECTURE#13
M
&C Morgan &cLaypool publishers
ABSTRACT
Quantum computers can (in theory) solve certain problems far faster than a classical computer
runninganyknownclassicalalgorithm.Whileexistingtechnologiesforbuildingquantumcomputers
are in their infancy,it is not too early to consider their scalability and reliability in the context of
thedesignoflarge-scalequantumcomputers.Toarchitectsuchsystems,onemustunderstandwhat
it takes to design and model a balanced, fault-tolerant quantum computer architecture.The goal
ofthislectureistoprovidearchitecturalabstractionsforthedesignofaquantumcomputerandto
explorethesystems-levelchallengesinachievingscalable,fault-tolerantquantumcomputation.
Inthislecture,weprovideanengineering-orientedintroductiontoquantumcomputationwith
anoverviewofthetheorybehindkeyquantumalgorithms.Next,welookatarchitecturalcasestudies
baseduponexperimentaldataandfutureprojectionsforquantumcomputationimplementedusing
trappedions.Whilewefocushereonarchitecturestargetedforrealizationusingtrappedions,the
techniques for quantum computer architecture design, quantum fault-tolerance, and compilation
described in this lecture are applicable to many other physical technologies that may be viable
candidates for building a large-scale quantum computing system. We also discuss general issues
involved with programming a quantum computer as well as a discussion of work on quantum
architecturesbasedonquantumteleportation.Finally,weconsidersomeoftheopenissuesremaining
inthedesignofquantumcomputers.
KEYWORDS
quantum computing,computer architecture,fault tolerance,error correction,trapped
ions, teleportation, qubit, quantum logic array, quantum simulation, quantum algo-
rithms
vii
Contents
Preface .................................................................. xi
1 Introduction ..............................................................1
2 BasicElementsforQuantumComputation ..................................7
2.1 Classicalvs.QuantumSignalStates(bitsvs.qubits) ......................... 7
2.2 LogicOperationsandCircuits............................................ 8
2.3 QuantumMeasurement ................................................ 13
2.4 Example:The3-QubitQuantumToffoliGate ............................. 15
2.5 Example:QuantumFourierTransform(QFT) ............................. 16
2.6 Example:QuantumTeleportation........................................ 17
2.7 Example:Deutsch’sQuantumAlgorithm ................................. 17
2.8 QuantumEntanglementandEPRPairs .................................. 19
2.9 OtherModelsofQuantumComputation ................................. 21
3 KeyQuantumAlgorithms ................................................ 23
3.1 QuantumIntegerFactorization .......................................... 23
3.1.1 TheIntegerFactorizationProblem................................. 23
3.1.2 AQuantumIntegerFactorizationAlgorithm ........................ 24
3.1.3 QuantumIntegerFactorization:ProofofClassicalPart ............... 25
3.2 OrderFinding ........................................................ 25
3.2.1 OrderFindingasQuantumEigenvalueEstimation................... 27
3.2.2 OrderFinding:ContinuedFractions ............................... 29
3.3 QuantumPhaseEstimation ............................................. 31
3.3.1 ProofSketchoftheCorrectnessofthePhaseEstimationCircuit ....... 31
3.4 EigenvalueEstimation ................................................. 34
3.5 TheHiddenSubgroupProblem.......................................... 36
3.6 Grover’sAlgorithmforQuantumSearch.................................. 38
3.6.1 SearchingwithaQuantumBlackBox .............................. 39
3.6.2 Grover’sAlgorithm .............................................. 39
3.6.3 ProofSketchoftheCorrectnessofGroverIteration .................. 40
viii
3.7 QuantumAdiabaticAlgorithms ......................................... 44
3.7.1 3-SAT:AnexampleofaQuantumAdiabaticalgorithm ............... 46
4 BuildingReliableandScalableQuantumArchitectures...................... 49
4.1 Reliableandrealisticimplementationtechnology ........................... 51
4.1.1 OpticalQuantumComputation:PhotonsasQubits .................. 53
4.1.2 Trapped-IonQuantumComputation:IonsasQubits ................. 54
4.2 RobustErrorCorrectionandFault-TolerantStructures...................... 57
4.2.1 NoiseModelAssumptions........................................ 58
4.2.2 ErrorCorrection:BasicsandNotation.............................. 61
4.2.3 Example:TheSteane[[7,1,3]]Code ............................... 67
4.2.4 LogicalQubitsinQuantumComputation .......................... 71
4.2.5 QuantumErrorCorrectionandFault-Tolerance:TheThresholdResult . 72
4.2.6 TheCostofQuantumErrorCorrection ............................ 75
4.2.7 Scale-UpinSystemSizeduetoErrorCorrection .................... 75
4.2.8 ErrorCorrectionSlowdown....................................... 76
4.3 QuantumResourceDistribution ......................................... 79
4.3.1 PhysicalQubitMovement ........................................ 80
4.3.2 Teleportation-BasedCommunicationandQuantumRepeaters......... 81
5 SimulationofQuantumComputation ..................................... 85
5.1 SimulationofErrorPropagation ......................................... 86
5.2 StabilizerMethodforQuantumSimulation ............................... 89
6 ArchitecturalElements .................................................. 91
6.1 QuantumProcessingElements(PE’s) .................................... 93
6.2 QuantumMemoryHierarchy ........................................... 94
6.3 QuantumAddressingSchemeforClassicalMemory........................ 97
6.4 ErrorCorrectionandQuantumArchitectureDesign........................ 99
6.4.1 EffectsofAncillaPreparationandLayout........................... 99
6.4.2 OptimizingErrorCorrectionalongCriticalPaths ................... 101
7 CaseStudy:TheQuantumLogicArrayArchitecture ....................... 103
7.1 QLAArchitectureOverview ........................................... 103
7.2 TheLogicalQubitDesignintheQLA .................................. 105
7.3 LogicalQubitInterconnect ............................................ 107
7.4 CompressedQLAArchitecture:CQLA ................................. 117
ix
7.4.1 TheGainProduct:ArchitecturePerformanceComparison ........... 120
7.4.2 CommunicationIssues:ExecutingtheToffoliGate.................. 120
7.4.3 MemoryHierarchyintheCQLAArchitecture ..................... 122
7.4.4 SimulatingtheCacheintheCQLA............................... 124
7.5 Qualypso ............................................................ 126
8 ProgrammingtheQuantumArchitecture ................................. 129
8.1 Physical-LevelInstructionScheduling ................................... 130
8.2 High-LevelCompilerDesign .......................................... 132
8.3 Architecture-IndependentCircuitSynthesis .............................. 133
8.4 MappingCircuitstoArchitecture ....................................... 134
8.5 OptimizationoftheLogicalQubitTiles ................................. 138
8.5.1 TheFault-TolerantThresholdEstimates ........................... 138
8.5.2 CircuitSchedulingandTheFault-ToleranceConstraint.............. 140
8.5.3 ThresholdCalculations.......................................... 143
8.5.4 SummaryDiscussion............................................ 145
9 UsingtheQLAforQuantumSimulation:TheTransverseIsingModel ....... 149
9.1 TheTransverseIsingModelOverview ................................... 149
9.2 TIMQuantumSimulationResourceEstimates ........................... 150
9.2.1 Phaseestimationcircuit ......................................... 150
9.2.2 DecompositionoftheTIMquantumcircuitintofault-tolerantgates ... 152
9.3 MappingtheTIMcircuitontotheQLAarchitecture ...................... 155
9.3.1 Resourceestimatesforthe1-DTIMproblem ...................... 156
10 Teleportation-BasedQuantumArchitectures.............................. 159
10.1 ThecnotGateandSingle-QubitGatesthroughTeleportation ............. 161
10.2 TheArchitecture ..................................................... 163
10.3 ErrorCorrectionthroughTeleportation.................................. 166
11 ConcludingRemarks ................................................... 169
Bibliography........................................................... 171
Authors’Biographies ................................................... 191