Lesson4QuantumComputing(第四課量子計算)

Vocabulary(詞匯)ImportantSentences(重點句)QuestionsandAnswers(問答)Problems(問題)ReadingMaterial(閱讀材料)

May18,2000—Theworldofquantummechanicsgoesagainstthegrainofeverydayexperience.It’san“AliceinWonderland”realmbeyondtheonesandzeroesofclassicalcomputing.Butifwecanfigureouthowtoputthisworldtowork,itwouldleadtoatechnologicalquantumleap,allowingustosolveproblemsthatwouldtakemillionsofyearstofigureoutusingpresent-daycomputers.AndthathashugeimplicationsfortheInternet—indeed,foranymeansofcommunicatingdata.

Present-daycomputingrestsonafoundationofbits,withinformationencodedwithinelectroniccircuitryasaseriesofonesandzeroes.Butascircuitsbecomemoreandmoreminiaturized,computerscomeclosertothefuzzythresholdofquantumphysics:Quantumobjects,suchaselectronsandothersubatomicparticles,canbethoughtofasexistinginmultiplestatessimultaneously:“up”aswellas“down”…“1”aswellas“0.”[1]Whenyouobserveaquantumobject,youtakeasnapshotofoneofthosestates—butyoualsodestroyquantuminformation.

Thisquantumrealmservesasthelowerlimitforclassicalcomputing.The“one-or-zero”conceptwon’tworkinaworldoffuzzy“one-and-zero”bits.

Butthisproperty,knownas“superposition,”opensthewaytoacompletelydifferentapproachtocomputing.Inthisapproach,onequantumbit—orqubit—enablesyoutomanipulatetwovaluesatthesametime.Asyoustringtogethermoreandmorequbits,thepowergrowsexponentially.Ifyoulinktwoqubitstogether,youcanworkwithfourvaluesatthesametime.Threequbitscanworkwitheightvalues,andsoon.Ifyoucangetupto40qubits,youcouldworkwithmorethanatrillionvaluessimultaneously.1Code-breaking

Whatcouldsuchcomputersbeusedfor?Oneimportantapplicationwouldbetofindtheprimefactorsofverylargenumbers.

Thisisn’tjustanemptymathematicalexercise.Primefactorizationhappenstobethefoundationforsecuredatacommunications.It’srelativelyeasytomultiplytwoprimenumberstogether(7,817and7,333,forexample),butnoonehasfoundaneasywaytodothecalculationinreverse—thatis,figureoutwhichtwoprimenumberscanbemultipliedtogethertoequal57,322,061.

Thisiswhatmakespublic-keycryptographypossible.Otherpeoplecansendyoumessagesthatarecodedusingtheproductoftwoprimes,butthatsecretmessagecanbedecipheredonlybysomeonewhoknowsthetwoprimefactors.[2]

Yourcomputerautomaticallyhandlesallthiscodinganddecodinginasecureelectronictransaction.That’swhatprotectsyourcreditcardinformationfromelectroniceavesdropperswhenyoubuysomethingovertheInternet.Butsupposetheeavesdroppershadquantumcomputers:Withallthatcomputingpower,theycouldfigureouttheprimefactorsofevenincrediblylargenumbers—andcrackthecode.Thus,thedevelopmentofquantumcomputerswouldrequireacompletechangeinthemethodsusedtoprotectinformationtransmittedovertheInternetandother“secure”communicationslinks.2Code-making

Fortunatelyforcode-makers,quantumcomputingtechniquescouldbeusedaswelltoguaranteesecurity(atleastwithinanegligiblysmallprobability).Quantumcryptographyrestsonthefactthatquantuminformationcannotbemeasuredwithoutdisruptingit.Thesecret-messagesoftwarecouldbebuiltsothatattemptstoeavesdroponamessagewouldsetoffanalarm—andautomaticallyshutdowntransmission.

Anotherfeatureusefulforquantumcryptography—andessentialforquantumcomputing—isabizarrecharacteristiccalledentanglement.Twoquantumobjectscanbelinkedtogethersothatifyouobservetheresultofaninteractionwithoneoftheobjects,youcanfigureoutwhatthestateoftheotherobjectisaswell.[3]

Theentanglementholdsevenifthetwoobjectsarewidelyseparated.

Thismakespossiblean“action-at-a-distance”phenomenonoftencalledquantumteleportation—atermthatoftenleadspeopletothinkof“StarTrek”transporters.Inreality,what’sbeingteleportedisinformationaboutaquantumobject,nottheobjectitself.

Twopeoplecouldencodeinformation,tradeitbackandforth,andreconstructtheinformationusingentangledquantumsystems.Evenifeavesdroppersinterceptthecodedinformation,theycouldn’treadthemessagebecausetheywouldn’tbepartoftheentangledsystem.3MakingItReal

Whatformsdothesequantumsystemstake?Photons,ionsandatomicnucleialreadyarebeingputtowork,withthespinofthoseparticlesrepresentingonesandzeroessimultaneously.

ResearchersattheLosAlamosNationalLaboratoryhavedemonstratedaquantumcryptographyschemethatworksover30miles(48kilometers)ofopticalfiber.AttheNationalInstituteofStandardsandTechnology,twotrappedberylliumionshavebeenwiredtogetherthroughentanglement,potentiallyrepresentingtheworld’sfirsttwo-qubitcomputationaldevice.

Inadditiontoiontraps,nuclearmagneticresonancedevicesarehelpingscientistsusethespinofatomicnucleiinquantumcomputingexperiments.Thereareevenproposalstomakequantumcomputingdevicesoutofgoodoldsilicon.

PeterShor,anaward-winningmathematicianatAT&TLabs,saysitmaybepossibletodevelopa30-qubitcomputerwithinthenextdecade—butthatwouldbejustthestart.Itwouldtakehundredsorthousandsofnetworkedqubitstosolveproblemsbeyondthecapabilityofclassicalcomputers.Nooneknowswhenwe’llbeabletoreachthatpoint.Infact,someresearchersworrythatthetechnicalhurdlesaretoogreattoovercome.4ProblemsandSolutions

Gettingtheinformationout:Sincemeasurementdestroysquantuminformation,howdoyouactuallygettheresultsofyourcalculations?Theoutputfromaquantumcomputermightwellbeanalogoustoaninterferencepattern,Shorsays:Thecorrectanswerwouldbebuiltupthroughconstructiveinterference,whileincorrectanswerswouldbecanceledoutthroughdestructiveinterference.[4]

Scalingupthesystem:TheNISTexperimentshowsthatqubitscanbelinkedtogetherthroughentanglement,butcansuchnetworksbescaledupinsize?Quantuminformationhasatendencyto“leak”intotheoutsideenvironment,inaprocessknownasdecoherence.Thus,thequantumsystemhastobeisolatedfromoutsideinfluenceasmuchaspossible.

Compensatingforerrors:Nomatterwhatyoudo,quantumoperationsareinherently“noisy”.Howdoyoucorrectforerrors?Itturnsoutthatyoucanadaptclassicalerror-correctingtechniquestoquantumsystemstomakethemfault-tolerant.Iftheerrorrateislessthanonepartper10,000,youcanmakequantumcomputersworkeventhoughtheindividualoperationsyou’reapplyingtoyourqubitsaren’tperfectlyaccurate,Shorsays.

Ifwedodevelopworkablequantumcomputers,theywouldcomeinhandyformuchmorethancode-breakingandcode-making.Theycouldmakeiteasiertofindsolutionstoother“needle-in-a-haystack”problems—problemsforwhichnobetterapproachisknownthanexhaustivelysearchingalargesetofpossiblesolutionsforthecorrectone.[5]Wecouldgainnewinsightsintohowmolecules,atomsandsubatomicparticlesbehave—unlockingsecretsofthequantumworlditself.

Butintruth,wecan’timagineallthepotentialusesforquantumcomputingtoday—anymorethanthecreatorsofthefirstdigitalcomputers,ahalf-centuryago,couldhaveimaginedwheretheirpioneeringworkwouldeventuallylead.

1．quantumleapn.[物]量子躍遷,<喻>躍進,巨大突破。

2．implicationn.牽連,糾纏;含蓄,含意,暗示;【數】蘊涵(式);?[pl.]推斷;結論。

3．subatomicadj.小于原子的；亞原子的，次原子的。

4．snapshotn.快照,快相；簡短描述；一晃眼；【計】抽點打印；瞬象。

5．superpositionn.重疊,重合,疊合。

6．qubit=quantumbit量子位。Vocabulary

7．factorizationn.因子分解(法),因式分解；編制計算程序。

8．cryptographyn.密碼使用法,密碼系統;密碼術。

9．deciphervt.譯解(密碼等),解釋n.密電譯文。

10．negligiblyadj.可以忽略的,不予重視的。

11．eavesdropv.偷聽n.屋檐水。eavesdroppern.偷聽者。

12．entanglementn.纏結;牽連；陷入困境;為難；[pl.](有刺)鐵絲網;障礙物。molecularentanglement分子纏結。

13．teleportationn.遠距離傳遞，遙傳：假定的傳遞方式，通常是指在瞬間讓事物或數據于某點消失再于另一點出現。

14．iontraps離子阱；離子閥。用來防止電子束中的離子擊中其它設備的一種裝置，例如一塊磁鐵。

15．spinofatomicnuclei原子核的自旋。

16．destructiveinterference相消(性)干擾,破壞性干擾。

17．decoherencen.【電】散屑;脫散。

18．“needle-in-a-haystack”problem“大海撈針”問題。

[1]Butascircuitsbecomemoreandmoreminiaturized,computerscomeclosertothefuzzythresholdofquantumphysics:Quantumobjects,suchaselectronsandothersubatomicparticles,canbethoughtofasexistinginmultiplestatessimultaneously:“up”aswellas“down”…“1”aswellas“0.”

但是隨著電路越來越小型化，計算機變得接近量子物理的模糊閾值尺寸：量子物體，如電子和其他亞原子的粒子，可以設想成多種狀態同時存在的情況，上升伴隨著下降，“1”與“0”共存。ImportantSentences

[2]Otherpeoplecansendyoumessagesthatarecodedusingtheproductoftwoprimes,butthatsecretmessagecanbedecipheredonlybysomeonewhoknowsthetwoprimefactors.

其他人可以通過這兩個素數的乘積來編碼發送信息，而只有知道這兩個素數因子的人才能解碼加密的信息。

[3]Twoquantumobjectscanbelinkedtogethersothatifyouobservetheresultofaninteractionwithoneoftheobjects,youcanfigureoutwhatthestateoftheotherobjectisaswell.

兩個量子目標可以鏈接在一起，因此如果你可以觀測到它們中間的一個和它們的交互作用的狀態，你就可以判斷出另一個的狀態。

[4]Theoutputfromaquantumcomputermightwellbeanalogoustoaninterferencepattern,Shorsays:Thecorrectanswerwouldbebuiltupthroughconstructiveinterference,whileincorrectanswerswouldbecanceledoutthroughdestructiveinterference.

量子計算機的輸出有充分的理由可以和干涉圖案類似，Shor說：正確的響應可以從相消干擾中建立，同時不正確的響應也可以從相消干擾中剔除。

[5]Theycouldmakeiteasiertofindsolutionstoother“needle-in-a-haystack”problems—problemsforwhichnobetterapproachisknownthanexhaustivelysearchingalargesetofpossiblesolutionsforthecorrectone.

他們能將其他一些“大海撈針”問題(那些除了從一組可能正確的結論中窮舉搜索而沒有其他一些好方法求解的問題)的求解變得容易些。

(1)Whichkindofcomputingrestsonafoundationofbits,withinformationencodedwithinelectroniccircuitryasaseriesofonesandzeroes?()

A.?Quantumcomputing.

B.?Present-daycomputing.

C.?Parallelcomputing.

D.?Distributedcomputing.QuestionsandAnswers

(2)?Public-keycryptographycan()messagescodedbyusingtheproductoftwoprimes,andthesecretmessagecanbedecipheredonlybysomeonewhoknowsthetwoprimefactors.

A.?send

B.?hide

C.?store

D.?synchronize

(3)?WhichofthefollowingsayingsisNOTTrue?()

A.?Primefactorizationhappenstobethefoundationforsecuredatacommunications.

B.?Itmaybepossibletodevelopa30-qubitcomputerwithinthenextdecade.

C.?Inreality,what’sbeingteleportedisinformationaboutaquantumobject,nottheobjectitself.

D.?Quantuminformationhasatendencyto“leak”intotheoutsideenvironment,inaprocessknownasiontrap.

(4)?Whichofthefollowingsisnotafeatureofquantumcomputing?()

A.?Existinginmultiplestatessimultaneously.

B.?Superposition.

C.?Quantumcryptography.

D.?Binarysystem.

(5)?Whatproblemofquantumcomputershouldbesolved?()

A.?“Needle-in-a-haystack”problems.

B.?Decoherence.

C.?Qubitsnetworksbescaledupinsize.

D.?Allofthem.1.?Whatcouldquantumcomputersbeusedfor？

2.Whatisan“action-at-a-distance”phenomenon?Problems

Althoughpracticalmachineslieyearsinthefuture,aformerlyfancifulideaisgainingplausibility.

ReadingMaterialAQuantumLeapforComputing

ByEricJ.LernerInBrief:

Systemsinwhichinformationobeysthelawsofquantummechanicscouldfarexceedtheperformanceofanyconventionalcomputer.Nowthattheprinciplesofquantumcomputinghavebeendemonstratedinthelab,IBMscientistsaretacklingtheformidabletaskofbuildingmachine.

Nomatterhowfastconventionalcomputersbecome,therewillalwaysbesomecalculationsthataretoolargeforthemtocompleteinreasonabletime.Hopingtocircumventtheselimitations,physicistshavebeguninthepastfewyearstoseriouslyentertainthepossibilitythataradicallydifferenttypeofcomputingcouldsolvecertainkindsofproblemsthataconventionalcomputercouldnotsolveinthelifetimeoftheuniverse.Called“quantumcomputing,”itharnessestheoftennonintuitivequantumpropertiesofindividualatomsandphotonstostoreandprocessinformation.Althoughithadbeenrealizedsincethe1980sthatquantumcomputerscould,intheory,outperformclassicalmachines,quantumcomputingwasuntilfiveyearsagogenerallyconsideredanesotericareaofinterest.Now,thatperceptionischanging,accordingtoNabilAmer,whocoordinatesIBMResearch’squantumcomputingefforts.“Progresshasbeenimpressive,”hesays.“Quantumcircuitshavebeenconstructed,error-correctioncodeshavebeentestedexperimentally,andonekindofextremelyefficientquantumalgorithm—forsearchingdatabases—hasbeenverifiedinaprototypequantumcomputer.”1BeyondClassicalPhysics

Althoughquantumcomputingisbasedonphysicalideaselaboratedinthe1920s,therecognitionthatquantummechanicsmightbeusefulforcomputingonlydawnedonscientistsinthe1980s.Onereasonisthatthecomputersofthe1940sand1950swerebuiltfromvacuumtubesandotherdevicesthatwereclearlyinthemacroscopicrealm,suggestsIBMFellowCharlesBennett,oneofthecreatorsofthebroaderfieldofquantuminformationtheory.Quantumconceptssimplydidn’tappearrelevant.

Nevertheless,asphysicistsbegantoconsiderthephysicallimitsofcomputing,theyweregraduallyledtowardthequantumarena.First,IBMFellowRolfLandauerdiscovered,in1961,thatenergyisuseduponlyduringirreversibleoperations,onesinwhichinformationisdiscarded.Basedonthatwork,Bennettshowedin1973thatfullyreversiblecomputation,whichdidnotconsumeanyenergy,wastheoreticallypossible.Sincequantumcomputationsalsoarereversible,experiencegainedinreversibleprogramminginthe1970sand1980sprovedusefulfordesigningquantumalgorithms.

Thepathtowardquantumcomputingbeganin1980,whenPaulBenioffofArgonneNationalLaboratorypublishedaquantummechanicalmodelforcomputation.Twoyearslater,RichardFeynmanintroducedtheideathatanyphysicalsystemcouldbesimulatedwithaquantumcomputer.ItwasDavidDeutschatOxfordUniversitywho,in1985,firstproducedamathematicaldescriptionofauniversalquantumcomputer—amachinethatcouldbeconstructedoutofquantumelementsandwouldinsomewaysbesuperiortoaconventionalcomputer.Butafloodofinterestinthefielddidnotemergetill10yearslater.2What“Better”Means

Itwasthediscoveryofjusthowmuchmorepowerfulaquantumcomputercouldbethatsetoffthecurrentwaveofactivity.In1994,PeterShorofAT&TLaboratoriesinventedanalgorithmthatcouldtakeadvantageofquantumphenomenatofactorlargenumbersandcouldhencebeused,forinstance,tocracktheRSAPublicKeyCryptosystem,usedbygovernmentsandcorporationsaroundtheworldforsecurecommunication.AnimportantsimplificationofShor’salgorithmwassubsequentlymadebyDonCoppersmithofIBM’sThomasJ.WatsonResearchCenter.

RSAisbasedontheideathatitiseasytomultiplytwolargenumberstogetathird,butverydifficulttofactorthatthirdlargenumbertogetthefirsttwo.Withconventionalcomputers,thedifficultyoffindingthefactorsofanumberisbelievedtoincreaseexponentiallywiththenumberofitsdigits.A250-digitnumber,forexample,takesroughlyamilliontimeslongertofactorthana130-digitnumber.Bymakingthenumberlongenough,onecanensurethatnoconventionalcomputerwillfactorthenumberinanyreasonablelengthoftime.ButShorshowedthataquantumcomputercouldfactornumbersmuchfaster,becausethenumberofstepsitrequiresisproportionaltothesquareofthenumberofdigits.Factoringa250-digitnumberisthereforeonlyfourtimesashardforaquantumcomputerasa130-digitone.3BettingOnSuccess

Shor’sresultsgaveatremendousboosttothenascentfieldofquantumcomputing,andsubsequentlyotherquantumalgorithmswerediscoveredthatalsorevealedaninherentadvantageofquantumcomputingforsolvingcertainkindofproblems.Suchconcepts,however,couldneverbeputtothetestwithoutaworkingquantumcomputer,andneitherShor’snortheotheralgorithmicworkaddressedthequestionofwhethersuchamachinecouldeverbebuilt.Butseveralgroupswerebettingthatitcould.

IBMwashometooneofthese.Intheearly1990s,Amerhadassembledasmall,informal“alternativesforcomputing”groupatWatsontolookatwhatthenextstepsincomputingmightbe.Togetthemembersthinkingasbroadlyaspossible,hechallengedthemwiththequestion,IfGodhadnotmadesilicon,howwouldwebuildcomputers?Afterexaminingvariousideas,Amersays,“wedecidedtofocusonquantumcomputingbecausewethoughtitpromisingandbecausewehadasolidbaseofexpertiseinthefieldofquantuminformation.”4TheWorldofQubits

Whatmakesaquantumcomputersodifferentfrom—andpotentiallysomuchmorepowerfulthan—aconventionalmachineisthepeculiarnatureofquantumbits,orqubits.Aqubitistheinformationunitprocessedbyaquantumcomputer.Physically,itcanberepresentedbyanyquantumsystemthatcanexistintwodifferentstates.Butthankstotheveryunclassicalconceptsof“superposition”and“entanglement”,aqubitisnotlimitedtothevaluesof0or1.

Onechoiceofaqubitmightbeanelectronspinninginamagneticfield.Wheneverthespinismeasured,itisalwaysfoundtobeeitheralignedwiththefield(“spin-up”state)oroppositetothefield(“spin-down”state).Butwhentheelectronisessentiallyisolatedfromtheenvironment—asitmustbeinaquantumcomputer—itbehavesasifitweresimultaneouslyinbothupanddownstates,withadiscreteprobabilityofbeinginthespin-upstateandanotherprobabilityofbeinginthespin-downstate.Thisphenomenonisknownassuperpositionofstates.

Entanglementistheothermainquantummechanicalprincipleuponwhichquantumcomputingrests.Apairofparticles,suchastwoelectronswithupanddownspins,canbeentangled—preparedinsuchawaythatthespinofoneelectronisguaranteedtobetheoppositeoftheother’s.Whatmakesthissostrangeisthat,untiloneoftheparticlesismeasured,neitherhasadefinitespindirection.Yet,assoonasoneismeasuredandfound,say,tobespinup,theotherwillbeknowntobeinthespin-downstate.Aslongasthetwoparticlesremainisolated—nomatterhowfaraparttheymaybe—theywillremainentangled,andmeasuringthestateofonewillimmediatelyprovideknowledgeaboutthestateoftheother.

Whiletheprobabilitiesoftheoutcomeofameasurementcanbecalculatedinadvance,theactualresultcannotbeknownbeforehand.Intuitively,onewouldnotexpectalackofpredictabilitytobeusefulforcomputing,butsuperpositionandentanglementarevaluablebecausetheygeneratearapidlyincreasingnumberofstatesasmorequbitscomeintoplay.So,whilea2-bitclassicalregistercanbeinonlyoneoffourpossiblebinaryconfigurations(00,01,10or11),aquantumregisterconsistingoftwoqubitscanstoreallfournumbersatthesametime,sinceeachqubitrepresentstwovalues.

Addingmorequbitsincreasestheregister’scapacityexponentially.Aquantumcomputercanthenperformlogicoperationson2ninputsinasinglecomputationalstep.Toperformthesametaskwithaclassicalcomputer,2nprocessorswouldhavetoworkinparallel,orelsethecomputationwouldhavetoberepeated2ntimes.Thisisthebasisforwhatisoftenreferredtoasquantumparallelism.5TwobyTwo

Aquantumcomputerisanapparatusinwhichthestatesofthequbitscanbemadetoevolveinadeterministicwayandtherebycarryoutacomputationbyoperatingonthequbitswithquantumlogicgates.Atfirst,itwasthoughtthattoperformthelogicaloperations,atleastthreequbitswouldhavetobemadetointeractinasinglegate,inamannersimilartoaclassicalANDgate,whichbringstogethertwoinputstoproduceanoutput.But,whileitisdifficulttomaketwoelectronsorotherparticlesapproachandwithdrawfromoneanotherprecisely,itisvirtuallyimpossibletodosowiththreeparticlessimultaneously.

SoonafterShor’salgorithmwaspublished,DavidDiVincenzoatWatsonfoundawayaroundthisproblem.Inwhatrepresentsoneofthemostimportantstepstowardapracticalcomputer,DiVincenzodemonstratedthatbringingpairsofparticlestogetherwouldbesufficienttocarryoutanylogicaloperation,evenoneinvolvinghundredsorthousandsofqubits.6QuantumHardware

Althoughtherearemanypossiblesystemsthatwouldserveasqubits,attentionhasfocusedonasmallnumberofpromisingones.AtIBM’sAlmadenResearchCenter,twoprojectsarecurrentlyunderwaytobuildactualquantumcomputers.Oneisbasedonions,theotheronspinningnuclei.“Iontraps”useelectromagneticforcestosuspendindividualions(atomslackingoneormoreelectrons)inanultrahighvacuum,isolatingthemfromtheirenvironmentsothatthesuperpositionoftheirstatescanevolveandinteract.Laserbeamsareusedtoswitchtheion’senergylevelsbetweenthe0and1statesaswellastopermittheionstointeract.Currently,Almaden’sRalphDeVoeisconstructingasimplequantumlogicgatecontainingafewionsinasingletrapthatwillprovideasophisticatedtoolfortestingfundamentaltheoriesofquantumcomputing.

Beginningin1996,IsaacChuang,nowatAlmaden,andNeilGershenfeldofMIT’sMediaLabpioneeredanotherapproach,basedonnuclearmagneticresonance(NMR)technology.Thisphysicalprocess—whichinvolvesorientingandmeasuringthespinsofatomicnucleiinamagneticfield—istheonethatservesasthebasisformedicalmagneticresonanceimaging(MRI)machines.

Nucleimakealmostperfectqubits,aswasfirstpointedoutbyDiVincenzoin1995.Likeelectrons,theycanhavespin-upandspin-downstates,but,inaddition,thesuperpositionsofnuclearspinstatestypicallylastmuchlongerthanthoseofelectronstatesorofmostotherphysicalsystems,thusallowingmoretimeforquantumcomputation.However,suchgoodisolationalsomeansthatlargenumbersofnuclei,about1018,areneededtobeabletocreateanobservablesignal.Sincethesenucleiarenearlyrandomlyorientedatroomtemperature,mostNMRapplicationsneverexplorethequantumbehaviorofnuclei.

ButChuangandGershenfelddevelopedanewmethod,usingtraditionalNMRtools,thatmakestheroom-temperaturenucleibehaveasiftheywereinaverycoldsystem,sothatallthemeasuredspinsappeartobeorientedinthesamedirection.ThispermitsobservationofthequantumbehaviorofnuclearspinsinmoleculesandhenceprovidesabasisforquantumcomputationwithNMR.Thenewmethod,whichuseschloroformmolecules,appliestworadio-frequencypulsesofdifferentdurationstocontrolthespinstates.Apulseofacertainlengthflipsaspinfromuptodown,whereasapulseofhalfthatdurationcreatesasuperpositionstateofupanddown.

Calculationscanbeperformedbecausethespin’sevolutionaftertheflipisinfluencedbythestateofadjacentatomsinthesamemolecule.Iftheadjacentatoms’nuclearspinisup,thenasecondhalfpulse,appliedafteranappropriateevolutiontime,willflipthespinofthefirstnucleusdown.Iftheadjacentnuclearspinisdown,thesamehalfpulsewillresultinanupspin.Thisiswhatcomputerscientiststerman“exclusiveORgate”.

ChuangandGershenfeldusedasequenceofsuchpulsestoimplementaquantumalgorithminventedbyLovGroverofLucentTechnologies’BellLabs.Thealgorithmallowsdatabasestobesearchedfasterthanispossiblewithconventionaltechniques.Forexample,tofindaniteminalistofnentrieswouldtakeaclassicalcomputer,onaverage,n/2tries.Grover'salgorithmonaquantumcomputerreducesthenumberoftriestothesquarerootofn.AlthoughChuangandGershenfeld’simplementationinvolvedonlytwoqubits,itwasthefirsttimeaquantumcalculationofanysizehadbeenperformed.Itprovedthatquantumcomputingcanwork.7MoreQubits

Othergroupsaroundtheworldhaveinitiatedexperimentsinquantumcomputing.Caltech,Stanford,Oxford,LosAlamosNationalLaboratory,theNationalInstituteofStandards,theUniversityofInnsbruckandtheUniversityofCaliforniaatBerkeleyaredevelopingimplementationsaimedathandlingafewqubits.Howeve