CFDI-為什么美國需要支持近期量子計算應用（英文）-2021.5-36正式版

WhytheUnitedStatesNeedstoSupportNear-TermQuantumComputingApplications

Asquantumcomputinghasthepotentialtotranscendthecurrentcomputationalboundariesthathavehadatransformationalimpactontheeconomyandsociety,beingaleaderinthistechnologyisofstrategiceconomicandsocialimportancetotheUnitedStates.

ByHodanOmaar|April27,2021

Quantumcomputingleveragesprinciplesfromquantummechanics,abranchofphysicsconcernedprimarilywiththeuniquebehaviorsofsubatomicparticlessuchaselectronsandphotons,toenablenew,extremelypowerfulcomputingarchitectures.Quantumcomputersusequantumbits(qubits),whichoperateaccordingtothequantumlawsof“superposition”and“entanglement,”thatenablethemtodothingstraditionalcomputerscannot.Becausequantumcomputingisstillearlyinitsdevelopmentphase,manyassumethatpracticalapplicationsarestillyearsaway.Inreality,asthisreportdocuments,organizationsarealreadyusingquantumcomputerstodayinreal-worldapplications.Asothernationsrapidlyscaleuptheirinvestmentstodevelopandusequantumcomputing,U.S.policymakersshouldensuretheUnitedStatesremainsaleader.Inparticular,investinginnear-termquantumcomputingapplicationswouldbolsterthedevelopmentoflonger-termusecasesofthetechnology,therebyhelpingtocementU.S.economiccompetitivenessandprotectnationalsecurity.

INTRODUCTION

Recentadvancesinquantumcomputingtechnologieshaveledtoawaveofinterest,bringingwithithypeandconfusionaboutboththepotentialofquantumcomputinganditscurrentstatus.Whilelarge-scalequantumcomputerscould,intheory,conductsuchfeatsasdecryptingcurrentcryptographicciphers,inreality,quantumtechnologiesarestillintheveryearlystages.JohnPreskill,aprofessoroftheoreticalphysicsatCaltechUniversityandaleadingscientistinquantumcomputing,noted—in2018that“weareenteringapivotalnewerainquantumtechnology”anerahereferredtoasthe“NISQera.”NISQstandsfornoisyintermediate-scale

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quantumtechnologyandreferstothefactthatthesystemsthatwillbeavailableoverthenextfewyears,willberelativelysmallinsize,andhaveimperfections(ornoise)thatwilllimitwhattheyareabletoachieve.

Overcomingtechnicalchallengesonthepathtowardlarge-scalequantumcomputerswilldependontheabilitytoscalethenumberofqubitsinquantumsystems,muchlikemodernclassicalcomputershavedependedonthegrowthinthenumberoftransistorsinsuperconductingchips.Thecurrententhusiasmforquantumcomputingcouldleadtoavirtuouscycleofprogress,asthesemiconductorindustryhasalreadyseen,butonlyifnear-termapplicationsforthequantumcomputingtechnologiesunderdevelopmentaresuccessful.TheU.S.governmentcanbestsupportthescalingofcurrentquantumtechnologiesbyfosteringacommercialmarketfortheminthenearterm.

Currentquantumdevicescanalreadysolveproblemsinanarrayofapplicationareas,suchashealthcare,manufacturing,transportation,andtheenvironment.Researchershaveidentifiedseveralotherpotentialapplicationareas,butthesefindingsremainintheresearchspace.Toensurequantumresearchiseffectivelytranslatedintoreal-worldapplications,Congressshouldprovide$500millioninfundingover5yearsforacademicresearchprojectsthathavenear-termapplicationstoworkwithindustryonresearchanddevelopment(R&D).Ideally,thisprogramwouldencourageandsupportresearchprojectsthatalignwithregionaleconomicdevelopmentgoalsbyfosteringcollaborationandpartnershipsbetweenuniversities,localbusinesses,andstateandlocalgovernments.

Theprovenadvantagesofusingquantumcomputersforoptimizationproblemssuggestthatthesesystemsmayalsohelpsolveclassificationproblemsbyimprovingartificialintelligence(AI)models.AItechnologies,suchasmachinelearning,deeplearning,neuralnetworks,andcomputervision,relyontheprocessingoflargeamountsofdatatoidentifypatterns.WhileclassicalsystemscanuseparallelismtotrainAImodelsonlargedatasets,somedatasetsaretoolargeortoocomplextobesolvedefficiently.Quantumcomputingcouldhelpaddressthischallenge.Quantumsystemsusequantumprinciplestocreatenon-classicalcorrelationsbetweendatapoints(calledentanglement),whichsuggeststheymightalsobeabletorecognizehighlycomplexrelationshipsindatasetsthatclassicalsystemscannot.Google’sAIQuantumteamisalreadyexamininghownear-termquantumcomputerscanimproveneuralnetworks,whicharealgorithmsthatmimicthewaythehumanbrainrecognizesrelationshipsbetweendifferentdatasets.

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Becausequantumcomputersarehighlyspecialized,difficulttomaintain,andexpensivetodevelop,mostuserswilllikelyaccessthesesystemsthroughcloud-basedsolutions.Indeed,theprivatesectorisalreadyofferingcloud-basedaccesstoquantumcomputing,suchasAmazon

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BraketandMicrosoftAzureQuantum,thatallowsuserstolearn,build,anddeploysolutionsusingthelatestquantumcomputinghardware.

However,thecostofquantumcomputingmaybetoohighformanyacademicresearchersandthuslimittheirabilitytodevelopfuturetalentinthefieldandapplyquantumcomputingsolutionstoongoingwork.Toaddressthisproblem,CongressshouldestablishaNationalQuantumResearchTaskForcetoprovideacademicresearcherswithaffordableaccesstohigh-endquantumcomputingresourcesinasecurecloudenvironment,aswellasthenecessarytrainingtheyneedtomakethemostofit.ThistaskforcecouldbeanalogoustotheAIresearchtaskforcethatwasestablishedaspartoftheNationalAIResearchResourceTaskForceActof2020andconsistofmembersfromacademia,government,andindustry.

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Theirgoalshouldbetodeveloparoadmapforbuilding,deploying,funding,andgoverninganationalquantumcomputingresearchcloudthatcanaccelerateaccesstoquantumcomputingforresearchinthepublicinterest.TheNationalQuantumResearchTaskForceshouldalsoensureitconsidershowtoprovideequitableaccesstoquantumcomputingatHistoricallyBlackCollegesandUniversities(HBCUs)andMinorityServingInstitutions(MSIs).

TheU.S.governmentitselfshouldplayaroleinexploringquantumapplications,notonlytobettersolveagency-specificproblemsbutalsotosignalthebenefitsofdoingsototheprivatesector.Tothisend,theOfficeofScienceandTechnologyPolicy(OSTP)shouldissueaquantumchallengethatrequireseveryfederalagencytoidentifyatleasttwoexistingusecasesforwhichtheycanusequantumcomputing.Forinstance,theDepartmentofTransportation(DOT)couldidentifywaysquantumcomputingcouldhelpoptimizepublictransportationacrosscities.But,sincethisreliesonaccesstomobilitydatathatisoftenheldbyprivatecompanies,DOTshouldestablishaplatformthataggregatesandcentralizesmobilitydataacrosscities,whichpublicandprivateplayerswouldcontributeto.

Finally,eventhoughthedevelopmentofalarge-scalequantumcomputercapableofbreakingcryptographicprotocolsisatleastadecadeaway,Congressshouldconsiderincentivizingpost-quantumcryptographytransition(PQC)inthepublicandprivatesectorsthroughmechanismssuchasadedicatedfundtosupportstateandlocalgovernmentsintheirtransitioneffortsandacertificationschemeforcompaniesthatimplementPQCprotocols.Asthedevelopmentofquantumcomputingtechnologieswilllikelybecomeglobalizedindustries,theNationalQuantumCoordinatingOffice(NQCO)shouldpublishareportoutliningwhatthequantumsupplychainlooksliketodayandwhererisksarelikelytoemergetobetterinformfutureeconomicandnationalsecuritypolicies.

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QUANTUMCOMPUTINGISAMOREGENERALFORMOFCLASSICALCOMPUTING

Abasicelectroniccomputerismadeupofcircuits,whichareclosedloopsthroughwhichcurrentmoves,andtransistors,whicharemicroscopicdevicesthatopenandclosecircuitstocommunicateelectricalsignals.

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Together,circuitsandtransistorsformgates,whichactaselectronicswitchesthatperformsuchfunctionsasamplifyingorswitchingoffthesesignals.

Electricalsignalsareanalog,whichmeanstheirvalueschangesmoothlyovertime.Asthesesignalsmovethroughacircuit,theyinteractwiththeirphysicalenvironment,creatingdisruptionsorperturbationsoftheirvalue.Successivedisruptionstoananalogsignalcanaccumulateuntilthesignaldegradestothepointofuselessness.

Toavoidinformationloss,mostcomputercircuitsbeganoperatingondigitalsignalsratherthananalogsignalsinthe1960sand1970s.

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Thesecircuitsvieweachelectricalsignalashavingadiscrete,binaryvalueofeither0or1(called“bits”),ratherthanasacontinuousvaluethatcouldrepresentaninfinitenumberofpossibilities.Byencodingdigitalvaluesinelectricalsignals,circuitscanrejectanydisruptions,or“noise,”thatmayappear.

Figure1:Inputandoutputsignalsforananalogamplifieranddiscreteinverter

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Inadditiontothebit-likestructurescalledqubits,quantumcomputerscanalsousecircuits,butthesesystemsbehaveverydifferentlythanclassicalsystems.Whilequbitshavetwoquantumstates,analogoustotheclassicalbinarystates0or1,theycanalsoexistina“superposition”ofthetwo,meaningtheyareinacombinationofboththe0and1stateatthesametime(seebox1fordetailsontheprincipleofsuperposition).Importantly,therangeofstatesaqubitcantakearenotonlyalltherealnumbersbetween0and1,butcomplexnumberstoo,whicharenumberssuchas

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thesquarerootof-1,thatdonothavetangiblevalues.Thesetofvaluesasinglequbitcantakecanberepresentedbyasphere,asshownin

figure2.

Figure2:Visualizingthepossiblestatesofinputqubits

Superpositionallowsquantumcomputerstoworkonalargersetofnumbers,whichrepresentsalargerproblemspace,butalsocausesthemtobelessrobustintermsofnoiseandthereforemoreerror-prone.

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Forexample,whenoperatingonaninputsignalvalueof0.9,atraditionalcomputerwouldrecognizethisinputisalmostcertainlya1,soitcan“remove”thenoisethatmighthavecomefrominteractionswiththephysicalsystemandtreattheinputvalueasa1beforecomputingitsoutput.Butsinceaquantumcomputeracceptsanyvaluebetween0and1,thereisnowaytoknowwhetherthesignaliscorrectorifithasbeencorruptedbynoise.Itcouldbe1withsomenoise,oritcouldbe0.9withnonoise.Asaresult,qubitoperationscurrentlyhavemoresignificanterrorratesthanclassicalcomputersandthereforeneedtheirenvironmentstobemorepreciselycontrolled.

Superpositionisnotusefulonitsown.Onemustmeasureaquantumstatetoextractinformationfromit.Asbox1describes,thisismuchliketryingtogetinformationaboutthestateofatossedcoin,whichisinasuperpositionofbothheadsandtails.Togetanyinformationaboutwhetherthecoinlandsheadsortails,onemustcatchitandobserveit.Indoingso,thesuperpositionisdestroyed.Similarly,observingaquantumsystem,knownas“measurement,”—destroyssuperposition,andtheoutputqubitlooksjustlikeaclassicaloneitiseither0or1.

Aquantumcomputercanperformallthesamecomputationsofaclassicalcomputer.Butbecauseofhighcosts,quantumcomputingisnotasuitableoptionformostapplications.Itthereforeonlymakessensetousequantumcomputingoverclassicalcomputingwhentheadvantagesofdoingso

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outweighthesecosts.However,thereareacertainsubsetofproblems,namelyoptimizationproblems,thatquantumcomputerscansolvebetter,faster,andmoreefficientlythanclassicalcomputers.Andthereareparticularproblems,suchassolvingcertaindifficultmathproblems,thatquantumcomputerswillbeablesolveinthefuturethatclassicalcomputersneverwill.

Box1:TheSuperpositionandMeasurementPrinciples

Thesuperpositionprinciplesaysthataquantumsystem,likeanelectron,isinablendofmultiplestateswithsomeprobabilities.Toseethis,imagineflippingacoin.Whenitlands,itcanonlybeeitherheadsortails.But,whileitisstillintheair,itisflippingbetweenbeingheadsandtails.Whensomeonecatchesit,however,thereisa50percentchanceitwilllandheadsanda50percentchanceitwilllandtails.

Similarly,aqubitcanbeinoneoftwostates.Qubits,likeelectrons,protons,neutrons,andallotherquantumsystems,havethepropertyofpossessinganintrinsicmagneticdipolethatactsasacompassneedle.Thismeansquantumsystemscanbeconsideredlittlemagnetswithbothanorthandasouthpole.Theycaneitherbeorientedwiththenorthpoleinthe“up”directionorwiththesouthpoleintheupdirection,asshownin

figure3.

Inquantummechanics,thisorientationiscalledspin,andwhenthenorthpoleisorienteduptheparticleissaidtohavespinup.Conversely,whenthesouthpoleisorienteduptheparticlehasspindown.

Figure3:Diagramsofparticleswithupanddownspin.

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Quantumsystemsmovebetweenthesetwoorientationsjustasatossedcoinflipsbetweenheadsandtails.Therefore,atanygiventime,whilewearenotobservingthesystem,itisinacombination,or“superposition,”ofbothstates,withsomeassignedprobabilitieswecancallprobabilitiesAandB.

Intuitively,wewouldassumeprobabilitiesAandBwouldadduptoequal100percent,astheydointhecoinexample.But,inthequantumrealm,themathematicalruledefiningtheseprobabilitiessaysitisthesquareofprobabilityAandthesquareofprobabilityBthatmustequalto100percent.ThismeansprobabilitiesAandBcouldbenegative(sincethesquareofanegativeisapositive),illustratinghowquantumphysics,while

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accurate,iscounterintuitiveandnotexactlyanalogousorfamiliartoanythingweunderstandfromclassicalphysics.

Regardlessofhowcomplextheseprobabilitiesare,theyarestilljustprobabilitiesdescribinghowlikelyaquantumsystemistobeinacertainstate.Thekeypointtounderstandaboutsuperpositionisthatatanygiventime,aquantumsystemisacombinationofbothpossiblestatesatthesametime.

Observingaquantumparticle,aprocesscalled“measurement,”occurswhentheparticleinteractswithsomelargerphysicalsystemthatextractsinformationfromit.Measurementdestroysthesystem’ssuperpositionandforcesthequantumsystemtobeinoneofitstwostates.Thisismuchlikeapersoncatchingandlookingatatossedcoinandfindingittobeheads.Byobservingthecoin,theyhavecausedtheprobabilityoffindingitheadstochangefrom50percentto100percentandtheprobabilityoffindingittailstofallfrom50percentto0.Similarly,measuringaquantumsystem,likeanelectron,andfindingittobespinupforcestheprobabilityassignedtoitbeingspinuptochangefromprobabilityAto100percentandtheprobabilityoffindingitspindowntofallfromprobabilityBto0percent.

Thekeydifferencebetweenthecoinandthequantumsystemisthatwhenweleavethecoinaloneitisonlyinonestate:headsortails.Tochangeitsstate,wehavetoapplyenergytothecoinandtossitintheair.Quantumsystemsaretheopposite.Itisintheirverynaturetochangestateswhenleftcompletelyalone.Whenwechangetheenergiesactingonthesystem,weforcethesystemto“collapse”intoonestateortheother,destroyingthesuperposition.

Therefore,inordertomanipulateaquantumsystem,onemustcarefullycontrolitsenergyenvironmentbyisolatingitfromtherestoftheworldandapplyingenergyfieldswithintheisolationregiontoelicitaparticularbehavior.

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THEREARETWOWAYSTOPHYSICALLYBUILDAQUANTUMCOMPUTER

Tobuildafunctionalquantumcomputer,onemustcreateaphysicalsystemthatencodesandthencontrolsandmanipulatesqubitstocarryoutcomputations.Therearecurrentlytwoleadingtechnologiestodoso.

Thefirstapproachusesatomicions,suchasberylliumions,trappedinavacuumtorepresentqubits.

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Unliketraditionalcircuits,whereinbitsmovethroughdifferentcomponentsofthecircuit,qubits(i.e.,theions)inthismethodareheldinplaceandmanipulatedbyelectricfields.

Figure4

showsanexampleofachipcontainingtrappedions.

Figure4:IonQ’siontrapchipwithionssuperimposedoverit

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Thesystemhastobeheldinavacuumchamberinordertominimizeitsinteractionwiththeenvironment.Similarly,laserscooltheionstocryogenictemperaturessoastoimprovethevacuumenvironmentandreducetheimpactofintrinsicelectricalnoiseontheion’smotion.

Thesecond(andprimemethod)forbuildingaquantumcomputerusestheuniquepropertiesofsuperconductingmaterials.

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Whencertainmaterials,suchasthemetalniobium,becomeverycold,theylosetheirelectricalresistanceandareabletotransportelectronsandconductelectricity.Inparticular,theynotonlyactasuperconductorsbutstarttoexhibitquantummechanicaleffects.

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Thesemetalscanbeusedtocreatequantumtransistors,muchlikesiliconisusedtobuildclassicaltransistors.

Figure5

showsasuperconductingquantumcomputermadewithniobium.

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Figure5:D-WaveSystems’superconductingsystem

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Superconductingquantumcomputinghasseveraladvantagesoverquantumcomputingimplementedontrappedions.First,superconductingqubitsaresolid-stateelectricalcircuitsthatareeasiertocontrolbecausetheyaremanipulatedusingmicrowaves.Scientistscanthereforeuseeasilyaccessiblecommercialmicrowavedevicesandequipmentinsuperconductingquantumcomputingapplications.Second,becausepreparingsuperconductingcircuitsisbasedontheexistingmethodforfabricatingsemiconductorchips,thedevelopmentofhigh-qualitydevicescanleverageadvancedchip-makingtechnologies,whichisgoodformanufacturingandscalability.

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Quantumcomputers—whetherbasedontrappedionsorsuperconductingtechnologies—requiretemperaturesclosetoabsolutezeroinordertooperateproperly.Cryogenics,whichaddressestheproductionandeffectsofverylowtemperatures,isthereforeanindispensableenablingtechnologyforquantumcomputing.

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Today,inordertopreservequantumdata,mostquantumdevicesareensconcedincryogenicrefrigeratorsthatareconnectedtoothermachinerythatcontrolsthequbitsandtheirenvironmentusinganumberofcables.But,mostofthecryogenictechnologiescurrentlyavailableweredevelopedtosupportscientificresearch,notcommercialapplications.Developersofquantumcomputersandquantumapplicationsarethereforeconstrainedbywhatisthecurrentstateoftheartincryogenics.TheQuantumEconomicDevelopmentConsortium(QED-C),anindustry-ledconsortiumestablishedbytheNationalQuantumInitiativeAct,conductedaworkshopin2019thatidentified“cryogeniccapabilitiesthat,ifrealized,wouldacceleratethepaceofresearchandinnovationandenabledevelopmentanddeploymentofquantumtechnologies.”

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Policymakersneedtoensurethatadvancesinquantumtechnologiesarecoordinatedalongsideallofthetechnologiesinassociatedsupplychains.

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MOSTUSERSACCESSQUANTUMCOMPUTERSTHROUGHTHECLOUD

Becausequantumcomputersareveryspecializedandexpensivetodevelop,fewresearchersororganizationswilldevelopthesesystems

themselvesorbuyquantummachinesoutright—.Instead,mostwillaccessthesesystemsthroughquantumcloudsservicesthatprovidevirtualaccesstoquantumsystemsthroughexistingInternetinfrastructure.Bothiontrapandsuperconductingquantumcomputerarchitecturescanbevirtualized.

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IBM,forexample,beganmakingaccesstotheirNewYorkCity-basedsuperconductingquantumcomputeravailablethroughthecloudin2016.

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Similarly,IonQ,aMaryland-basedquantumcomputingcompany,isworkingwithAmazonWebServicesandMicrosoftAzuretomakeaccesstoitstrapped-ionbasedsystemavailable.

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THEREARETWOWAYSTOIMPLEMENTAQUANTUMCOMPUTER

Therearebroadlytwotypesofquantumcomputers.Analogquantumcomputersoperateonqubitsbydirectlymanipulatingtheinteractionsbetweenthemwithoutbreakingtheseactionsintodistinctoperations.

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Forthepurposesofthisreport,wefocusonlyononeofthemostadvancedanalogquantumcomputingapproaches:quantumannealing.Bycontrast,digitalquantumcomputersoperateonqubitsusingaseriesofoperations(orgates)inafashionsimilartoclassicalcomputers.

QUANTUMANNEALING

Classicalcomputersstruggletosolveoptimizationproblemsinwhichthegoalistofindthebestfeasiblesolution,becausetheseproblemsbecomeexponentiallymorecomplicatedasthenumberofpossiblesolutionsincrease.Forexample,iftheproblemistofindtheshortestroutebetween3cities,thereareonly6possiblesolutionstoconsider.Butifthereare50cities,therearemorethan1trillionsolutionstoconsider.

Quantumcomputersusethelawofphysicstosolveoptimizationproblemsmoreefficiently,astheseproblemseasilymaptoenergyminimizationproblems.Byexploitingthefactthatphysicalsystemsbynatureseektominimizetheirenergy(e.g.,objectsslidedownhills,hotthingscooldown,etc.),quantumcomputersframeanoptimizationproblemasanenergyminimizationproblemandsimulatetheingeniouswaysquantumsystemssolvethelatter.Certaintypesofquantumcomputeraredesignedtodoexactlythisthroughaprocesscalledquantumannealing.

First,asetofqubitsisusedtorepresentallthepossiblesolutionstoaproblem(see

figure6)

.Sinceeachqubitisinasuperpositionstateof0and1,asinglequbitcanrepresentaproblemthathastwopossiblesolutions,where0representsonesolutionand1representstheother;twoqubits

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canrepresentfourpossiblesolutions;threecanrepresenteightpossiblesolutions;andsoon,demonstratingthatthenumberofpossiblesolutionsqubitscanrepresentgrowsexponentiallyasthenumberofqubitsincrease.Thegoalisforeachqubittocollapseintothe0or1state,suchthatwhenallthequbitsaretakentogether,theyrepresentthelowestenergystateandthereforetheoptimalsolutiontoaproblem.

Figure6:Qubitsinasuperpositionstateatthestartoftheannealingprocess

Whileaclassicalcomputerwouldtryeverycombinationof0and1bitstofindtheoptimalsolution,quantumannealerscanmanipulateandbuildcorrelationsbetweenqubitssothattheyessentiallybecomeonelargequantumobject,asillustratedin

figure7.

Figure7:Entangledqubits

Thisisknownasquantumentanglement,aspecialpropertyofmultiqubitsuperpositionstatesthatmeansthequbitsbecomecorrelatedinsuchawaythatchangingthestateofonequbitinstantaneouslychangesthestateofanotherinapredictableway(seebox2fordetails—ontheprincipleofentanglement).Thisiscertainlyastrangeproperty—onethatAlbertEinsteindescribedas“spookyactionatadistance”butitisthekeyingredienttoquantumcomputers’speedadvantageoverclassicalcomputers.

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Tobeclear,quantumannealing(andquantumcomputingmoregenerally)isnotclassicalcomputingspedup.Rather,quantumannealinglooksatanoptimizationprobleminanewlight.Insteadofusingbruteforcetoworkouttheoptimalsolutiontoaproblem,quantumannealingexploitstheunderlyingpatternsbetweensystemsthatcanonlybeseenfromaquantumviewpoint.

Theoutcomeofmanipulatingthesecorrelationsisthat,eventually,thequantumobjectwillcollapseintotheminimumenergystate,representingtheoptimalsolutiontoanoptimizationproblem,asillustratedin

figure8.

Figure8:Qubitsinasuperpositionstateattheendoftheannealingprocess

Box2:TheEntanglementPrinciple

Undersomecircumstances,twoormorequantumobjectsinasystemcanbeintrinsicallylinkedsuchthatmeasurementofonedictatesthepossiblemeasurementoutcomesforanother,regardlessofhowfarapartthetwoobjectsare.Thepropertyunderlyingthisphenomenon,knownas“entanglement,”iskeytothepotentialpowerofquantumcomputing.

Tovisualizethis,considerthetwoentangledparticlesasapairofgloves.IfsomeoneweretochooseonegloveatrandomandsendittotheirfriendinParisandsendtheotherglovetotheirfriendinBerlin,wecanassumethateachfriendhasa50percentchanceofreceivingeitherglove.But,ifthefriendinParisweretorevealthattheyhadreceivedtherightglove,wewouldknowwithcertaintythatthefriendinBerlinhadreceivedtheleftglove,eventhoughtheyhadnottoldus.Similarly,entangledqubitscomeinpairs.Ifwemeasureoneandfindittobeinonestate(e.g.,spinup),wewillknowwithcertaintythattheotherparticleinthepairmustbeintheoppositestate(e.g.,spindown)withouthavingtodoanyfurthermeasurements.

Toseethepowerfulimplicationsofentanglement,considertwoelectronsthatwehaveyettomeasure(showninredandbluein

figure9)

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particle1andparticle2couldbeinspinup;orparticle1couldbeinspinupandparticle2couldbeinspindown;orparticle1inspindownandparticle2inspinup;or,bothparticlescouldbeinspindown.

Ifwewanttofindoutwhattheorientationofthispairofparticlesis,andwecannotmakeuseofthefacttheyareentangled,wemustconsiderallfouroptions.But,ifweknowtheelectronsareentangled,weonl