Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice

94 Pages·2014·5.152 MB·English

by  Catherine C. McGeoch

Adiabatic Quantum Computation
and Quantum Annealing
eoryandPractice

Synthesis Lectures on Quantum
Computing
Editor
MarcoLanzagorta,U.S.NavalResearchLabs
JeffreyUhlmann,UniversityofMissouri-Columbia
AdiabaticQuantumComputationandQuantumAnnealing:eoryandPractice
CatherineC.McGeoch
2014
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High-levelStructuresforQuantumComputing
JaroslawAdamMiszczak
2012
QuantumRadar
MarcoLanzagorta
2011
eComplexityofNoise:APhilosophicalOutlookonQuantumErrorCorrection
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2010
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DanielJ.Rogers
2010
QuantumComputerScience
MarcoLanzagortaandJeffreyUhlmann
2008
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2008
Copyright©2014byMorgan&Claypool
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin
anyformorbyanymeans—electronic,mechanical,photocopy,recording,oranyotherexceptforbriefquotations
inprintedreviews,withoutthepriorpermissionofthepublisher.
AdiabaticQuantumComputationandQuantumAnnealing:eoryandPractice
CatherineC.McGeoch
www.morganclaypool.com
ISBN:9781627053358 paperback
ISBN:9781627053365 ebook
DOI10.2200/S00585ED1V01Y201407QMC008
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONQUANTUMCOMPUTING
Lecture#8
SeriesEditors:MarcoLanzagorta,U.S.NavalResearchLabs
JeffreyUhlmann,UniversityofMissouri-Columbia
SeriesISSN
Print1945-9726 Electronic1945-9734
TrademarkNotices:
D-Wave,D-WaveOne,D-WaveTwo,Vesuvius,andQSagearetrademarksofD-WaveSystemsInc.
IntelandIntelXeonaretrademarksofIntelCorporation.
ILOGandILOGCPLEXareregisteredtrademarksofInternationalBusinessMachinesCorporation.
Adiabatic Quantum Computation
and Quantum Annealing
eoryandPractice
Catherine C. McGeoch
AmherstCollege
D-WaveSystemsInc.
SYNTHESISLECTURESONQUANTUMCOMPUTING#8
M
&C Morgan &cLaypool publishers
ABSTRACT
Adiabaticquantumcomputation(AQC)isanalternativetothebetter-knowngatemodelofquan-
tumcomputation.etwomodelsarepolynomiallyequivalent,butotherwisequitedissimilar:one
property that distinguishes AQC from the gate model is its analog nature. Quantum annealing
(QA)describesatypeofheuristicsearchalgorithmthatcanbeimplementedtoruninthe“native
instructionset”ofanAQCplatform.
D-WaveSystemsInc.manufacturesquantumannealingprocessorchipsthatexploitquan-
tumpropertiestorealizeQAcomputationsinhardware.echipsformthecenterpieceofanovel
computingplatformdesignedtosolveNP-hardoptimizationproblems.Startingwitha16-qubit
prototypeannouncedin2007,thecompanyhaslaunchedandsoldincreasinglylargermodels:the
128-qubitD-WaveOnesystemwasannouncedin2010andthe512-qubitD-WaveTwosystem
arrivedonthescenein2013.A1,000-qubitmodelisexpectedtobeavailablein2014.
ismonographpresentsanintroductoryoverviewofthisunusualandrapidlydeveloping
approachtocomputation.Westartwithasurveyofbasicprinciplesofquantumcomputationand
whatisknownabouttheAQCmodelandtheQAalgorithmparadigm.NextwereviewtheD-
Wave technology stack and discuss some challenges to building and using quantum computing
systemsatacommercialscale.elastchapterreviewssomeexperimentaleffortstounderstand
thepropertiesandcapabilitiesoftheseunusualplatforms.ediscussionthroughoutisaimedat
anaudienceofcomputerscientistswithlittlebackgroundinquantumcomputationorinphysics.
KEYWORDS
quantumcomputing,adiabaticquantumcomputation,quantumannealing,D-Wave
Systems,optimization,NP-hardproblems
vii
Contents
Acknowledgments...................................................ix
1 Introduction ....................................................... 1
1.1 What’sInside .....................................................3
1.2 WhatHappensNext?...............................................7
2 AdiabaticQuantumComputation...................................... 9
2.1 BasicsofQuantumComputation .....................................9
2.2 ComponentsofAQCAlgorithms ....................................15
2.2.1 ASimpleExample ..........................................16
2.2.2 eAdiabaticeorem.......................................18
2.3 AnAlgorithmforExactCover ......................................19
2.3.1 RuntimeAnalysis ...........................................21
2.4 ComplexityClasses ...............................................23
2.4.1 AQCandRelatedModels ....................................26
3 QuantumAnnealing................................................ 29
3.1 OptimizationandHeuristicSearch ...................................31
3.2 ClassicalImplementationsofQA ....................................35
3.2.1 IsingModelandRelatedProblems..............................36
3.2.2 GeneralSatisfiability.........................................39
3.2.3 TravelingSalesmanProblem...................................41
3.2.4 FactoringIntegers ...........................................41
4 eD-WavePlatform .............................................. 43
4.1 eUser’sView ..................................................43
4.2 eTechnologyStack .............................................49
4.2.1 QubitsandCouplers.........................................50
4.2.2 Topology ..................................................51
4.2.3 ControlCircuitry ...........................................53
4.3 Challenges ......................................................54
4.4 SomeAlternativeQuantumAnnealingSystems.........................56
viii
5 ComputationalExperience........................................... 59
5.1 WhatProblemscanitSolve? .......................................59
5.1.1 TrainingClassifiers ..........................................61
5.1.2 FindingRamseyNumbers ....................................62
5.1.3 ProteinFolding .............................................64
5.1.4 GeneralOptimization........................................65
5.2 IsItQuantum?...................................................66
5.2.1 QuantumAnnealingvs.ermalAnnealing ......................66
5.2.2 DemonstrationofEntanglement ...............................67
5.2.3 SignaturesofQuantumAnnealing..............................68
5.3 HowFastIsIt? ..................................................69
5.4 Epilogue ........................................................71
Bibliography ...................................................... 73
Author’sBiography ................................................. 83
ix
Acknowledgments
I would like to express my very great appreciation to those who patiently answered my many
questions,madethoughtfulsuggestionsaboutimprovingdraftmanuscripts,andcontributedjust
the right images for conveying complex ideas: Mohammad Amin, Andrew Appel, Paul Bunyk,
CarrieCheung,MarkJohnson,JeremyHilton,AndrewKing,JamieKing,TrevorLanting,Bill
Macready,LyleMcGeoch,MilesSteininger,JohnRager,GeordieRose,AidanRoy,andMurray
om.
CatherineC.McGeoch
July2014