QuantumComputing:Concepts,CurrentState,andConsiderationsforCongress

September7,2023

CongressionalResearchService

R47685

CongressionalResearchService

QuantumComputing:Concepts,CurrentState,andConsiderationsforCongress

CongresspassedandthePresidentsignedintolawtheNationalQuantumInitiativeAct(NQIAct;P.L.115-368;codifiedat15U.S.C.§§8801etseq.)inDecember2018toaccelerate

quantumresearchanddevelopment(R&D)fortheeconomicandnationalsecurityoftheUnitedStatesandensurethecontinuedU.S.leadershipinquantuminformationscienceandits

technologyapplications.SincetheenactmentoftheNQIAct,researchershavemadeprogressinquantumR&D.TheauthorizationoffundingforseveralfederalR&DactivitiesundertheNQIActissettoexpireattheendofFY2023.

SUMMARY

R47685

September7,2023

LingZhu

Analystin

Telecommunications

Policy

IntheNQIAct,Congressdefinedthetermquantuminformationscienceas“theuseofthelawsofquantumphysicsforthestorage,transmission,manipulation,computing,ormeasurementofinformation.”Quantumcomputing,oneoftechnologyapplicationsofquantuminformationscience,usesaquantumbit,orqubit,asitsbasicdataunit,toharnessquantum

propertiessuchassuperpositionandentanglement.Bygeneratingandmanipulatingqubits,aquantumcomputeriscapableof

performingcertaincalculationssignificantlyfasterthanconventional,non-quantumcomputers,knownasclassical

computers,leadingtonewwaystosolvesomecomplexproblemsthatwerepreviouslyunsolvable.Researchershavedemonstratedthepotentialforquantumcomputingapplicationsinareassuchascryptography,machinelearning,andscientificandengineeringresearch,particularlyusingmodeling,optimization,andsimulation.

TheNQIActistheprimaryfederallawthatsupportsR&Dactivitiesinquantumcomputing.Ithasbeenamendedbythe

NationalDefenseAuthorizationAct(NDAA)forFY2022(P.L.117-81)andtheCHIPSandScienceAct(DivisionBofP.L.117-167).Thecurrentactcontainsfourtitles,directing(1)thePresidenttoimplementanNQIProgramwitha10-yearplanto

acceleratequantumR&D,investinandcoordinatefundamentalfederalR&Dactivities,andpartnerwithindustryand

universitiestoadvancegoalsandprioritiesintheNQIProgram;(2)theNationalInstituteofStandardsandTechnology

(NIST)tocarryoutspecifiedR&Dactivitiesandconveneastakeholderconsortiumtoidentifythefuturemeasurement,

standards,cybersecurity,andneedsforarobustquantumindustry;(3)theNationalScienceFoundation(NSF)tocarryoutabasicresearchandeducationprogramandawardgrantstoestablishMultidisciplinaryCentersforQuantumResearchand

Education;and(4)theDepartmentofEnergy(DOE)toadministeranumberofprograms,includingabasicresearch

program,NationalQuantumInformationScienceResearchCenters,aprogramtoaccelerateinnovationinquantumnetworkinfrastructure,andtheQuantumUserExpansionforScienceandTechnologyprogram.TheauthorizationoffundingforthefollowingactivitiesundertheNQIActissettoexpireinSeptember2023:NSF’sfiveuniversity-basedQuantumLeap

ChallengeInstitutes,DOE’sfivenationallab-ledresearchcenters,andNIST’sR&Dactivities,includingtheindustry-ledQuantumEconomicDevelopmentConsortium.

SincetheenactmentoftheNQIActin2018,researchershavemadenotableadvancesinquantumcomputinginthreeareas:demonstratingthataquantumprocessorcouldexecuteacomplexcomputationaltaskmuchfasterthanaclassical

supercomputerinanexperiment;demonstratingthemitigationofcalculationerrorscausedbythelossofinformationheldby

qubits—amajoroutstandingchallengetoquantumcomputing—inanexperiment;andscalingupquantumcomputingprocessors,thusenhancingtheirpowerandpotentialreliability.

SomeexpertsarguethatsustainedfederalR&Dinvestmentisnecessarytoaccelerateprogresstowardpracticalquantum

computingandtomaintaintheleadingroleofU.S.researchersandinstitutionsglobally.Thereislessconsensus,however,onthespecificrolethefederalgovernmentshouldplayinquantumR&Dandhowresourcesandsupportshouldbespecificallytargetedandprioritized.

Congressfacespolicymakinginthreeareas.First,Congressmaydecidewhetherandhowtoreauthorizeorexpandfederal

R&DactivitiesandsupportundertheNQIAct.Second,CongressmaychoosewhethertosetpolicyprioritiestoensureU.S.leadershipinquantumcomputing,including(1)acceleratingthedevelopmentofpracticalquantumcomputerswithnear-

term,usefulapplications;(2)supportingthedevelopmentofanaccessible,sustainable,andsecuresupplychainanddomesticmanufacturingcapabilities;and(3)facilitatingthedevelopmentofaquantum-literateworkforce.Congressmayalsoconsiderwhethertosetpolicyprioritiestoprotectnationalsecurityinterestsinquantumcomputingbyaddressingrisks;inparticular,

theanticipatedcompromiseofcurrentcryptographicsystemsthatprotectsensitivedataandcommunicationsamonggovernmentagencies,financialinstitutions,healthserviceproviders,andothers.

QuantumComputing:Concepts,CurrentState,andConsiderationsforCongress

CongressionalResearchService

Contents

ConceptsofQuantumComputing 1

TheCurrentStateofQuantumComputing 3

DemonstratingQuantumAdvantage 3

IncreasingQuantumComputingReliability 3

AchievingQuantumAdvantageforPracticalProblems 5

FederalLawConcerningQuantumComputing 6

FederalR&DInvestmentsinQuantumInformationScienceandTechnology 8

PolicyConsiderationsforCongress 9

ReauthorizingFederalR&DActivitiesUndertheNQIAct 10

EnsuringContinuedU.S.LeadershipinQuantumComputing 11

AcceleratingtheDevelopmentofPracticalQuantumComputerswithNear-Term

Applications 11

SupportingtheDevelopmentofaQuantumSupplyChain 12

FacilitatingWorkforceDevelopmentforQuantumComputing 13

ProtectingNationalSecurityInterestsinQuantumComputing 14

Tables

Table1.R&DActivitiesAuthorizedintheNQIAct,asAmended 9

TableB-1.NSFQuantumLeapChallengeInstitutes(QLCI) 21

TableB-2.DOENationalQuantumInformationScienceResearchCenters 22

Appendixes

AppendixA.KeyTermsofQuantumComputingExplained 17

AppendixB.NQIAct-FundedR&DCenters 20

Contacts

AuthorInformation 22

QuantumComputing:Concepts,CurrentState,andConsiderationsforCongress

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C

ongresspassedandthePresidentsignedintolawtheNationalQuantumInitiativeAct(NQIAct;P.L.115-368;codifiedat15U.S.C.§§8801etseq.)inDecember2018toaccelerate

quantumresearchanddevelopment(R&D)fortheeconomicandnationalsecurityofthe

UnitedStatesandensurethecontinuedU.S.leadershipinquantuminformationscienceandits

technologyapplications.SincetheenactmentoftheNQIAct,researchershavemadeprogressinquantumR&D,whiletheauthorizationoffundingforseveralfederalR&Dactivitiesunderthe

NQIActissettoexpireattheendofFY2023.AsCongresscontemplateswhethertoreauthorizetheNQIActandcontinueappropriations,thereareanumberofquestionsitmayconsider:Whatisthecurrentstateofquantumtechnologies?HowfararecurrentR&Dactivitiesfromdeliveringusefulquantumsystemsandapplications?WhatresourcesareneededtoaccelerateR&Dinthe

fieldandhowshouldthoseresourcesbeprioritized?Howcanfederalagenciesfurthercoordinate

andfacilitateauthorizedR&Deffortsincollaborationwithindustry,academia,andglobalpartners?

Thisreportusesoneparticularquantuminformationtechnology—quantumcomputing—to

explainconceptssuchasquantumsuperposition,entanglement,andqubit,andthecurrentstateofthefield,includingrecenttechnicalmilestones.Thereportalsoprovidesanoverviewofrelevantfederallaws—theNQIActaswellasquantumprovisionsinannualNationalDefense

AuthorizationActs(NDAAs)andtheCHIPSandScienceAct.Finally,thereportdiscusses

currentpolicyissuesthatCongressmayopttoconsider:(1)reauthorizingfederalR&DactivitiesundertheNQIAct;(2)ensuringcontinuedU.S.leadershipinquantumcomputingthrough

acceleratingnear-termapplications,developingarobustsupplychain,andfacilitatingworkforcedevelopment;and(3)assessingandprotectingnationalsecurityinterestswithadvancesin

quantumcomputing.

ConceptsofQuantumComputing

Congresshasdefinedsomekeytermsrelatedtoquantumcomputinginfederallaw.IntheNQI

Act,thetermquantuminformationsciencemeans“theuseofthelawsofquantumphysicsforthestorage,transmission,manipulation,computing,ormeasurementofinformation.”1Inthe

QuantumComputingCybersecurityPreparednessAct(P.L.117-260),thetermquantumcomputermeansacomputerthat“usesthecollectivepropertiesofquantumstates,suchassuperposition,

interference,andentanglement,toperformcalculations.”2Inadditiontothesestatutory

definitions,reportsissuedundertheNationalQuantumInitiativeProgramestablishedintheNQI

Actusethetermquantuminformationscienceandtechnology(QIST)torefertothe

understandingandapplicationsofquantuminformationsciencetodesignnewtypesofcomputers,networks,andsensorsthat“enablenewspeed,precision,orfunctionality.”3

Specifically,quantumcomputing—partoftheumbrellaconceptofQIST—isanemerging

computingparadigmthatharnessestheprinciplesofquantummechanicstorepresent,store,

process,andtransmitdata.4Inquantumcomputingthebasicdataunitisaquantumbit,orqubit,

115U.S.C.§8801(6).

2Section3(9)ofP.L.117-260.

3NationalQuantumInitiative,AbouttheNationalQuantumInitiative:QIS—QuantumInformationScience,at

/about/#QIS

.SeealsoNationalQuantumInitiativeAdvisoryCommittee,Renewingthe

NationalQuantumInitiative:RecommendationsforSustainingAmericanLeadershipinQuantumInformationScience,June2023,p.3,at

/wp

-content/uploads/2023/06/NQIAC-Report-Renewing-the-National-

Quantum-Initiative.pdf.

4

SeeAppendixA

fortheexplanationforthetermsofquantumnetworkingandquantumsensing.

QuantumComputing:Concepts,CurrentState,andConsiderationsforCongress

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theequivalentofabitinconventional,non-quantumcomputers(alsocalledclassicalcomputers).5Aquantumcomputer’sdataprocessingpowerislargelycontingentupontheeffectiveand

efficientgenerationandmanipulationofqubits.6Scientistshavephysicallycreatedandcontrolledqubitsusingsuperconductingmaterialsanddevices,7ortinyobjectssuchasatoms,electrons,

trappedions,orphotons.8

Unlikeaclassicalbitthatcanrepresentonlyonepieceofinformation,either0or1,aqubitcan

representmoremathematically-richinformationbybeinginasuperposition,whichcanbe

expressedasacombinationofacertainprobabilityofbeingin0andacertainprobabilityofbeingin1.9Qubitscanbeentangledwithoneanother,sothataquantumcomputercanmanipulatea

groupofqubitsinasingleoperation,unlikeinclassicalcomputingwherethesameoperation

needstobeperformedoneachbitindividually.10Computeralgorithmsspeciallydesignedtotakeadvantageoftheseuniquequbitpropertiesofsuperpositionandentanglementwillallowquantumcomputerstoperformmultipletaskssimultaneouslyandcertaincalculationssignificantlyfaster

thanclassicalcomputers,leadingtonewwaystosolvesomecomplexproblemsthatare

intractableforclassicalcomputersatanyscale(evenhigh-performancesupercomputers).11

Inshort,asthenumberofqubitsincreaseslinearly,theinformationthatthequbitsarecapableofcarryinggrowsexponentially.Inclassicalcomputing,doublingthenumberofbitsonlydoublesitscomputationalpowertohandledata.See

AppendixA

fortheexplanationforthetermsof

quantum,quantummechanics,quantumsuperposition,andquantumentanglement.

Resolvingcomputationallycomplexproblemstypicallyrequiresdealingwithalargenumberofvariablesthatinteractincomplicatedways,withmultiplepossibleanduncertainoutcomes.12

Solvingtheseproblemsrequiresavastamountofcomputingresourcesandistime-consuming.Examplesincludemodelingthebehaviorofindividualatomsinamolecule;simulatingall

possibleinteractionswhentwoobjectscollidewitheachother;optimizingasetofroutesforafleetofvehiclestodeliverpackagestocustomersindifferentlocations;factoringalarge

compositeintegerintoaproductofprimenumbersincryptographicalgorithms;andidentifyingfraudpatternsinfinancialtransactions.Researchershavedemonstratedthepotentialforquantumcomputingtosolvecomplexproblemsinareassuchascryptography,machinelearning,and

scientificandengineeringresearch,particularlyusingmodeling,optimization,andsimulation(e.g.,forthestudyofquantumphysics,chemistry,andmaterialscience,andfornewdrug

5Abit,shortfor“binarydigit,”representsabinarycodeofeither0or1.Letters,numbers,symbols,images,andaudiosignalsareencodedincombinationsofbitstorepresentandstoreinformationinclassicalcomputers.SeeInjosoftAB,ASCIICharacters,at

/characters

.

6AmazonAWS,WhatIsQuantumComputing,QuantumTechnologies,2023,at

/what

-is/quantum-computing/.SeealsoMartinGiles,“Explainer:WhatIsaQuantumComputer?,”MITTechnologyReview,January29,2019,at

/2019/01/29/66141/what

-is-quantum-computing.

7OlivierEzratty,“PerspectiveonSuperconductingQubitQuantumComputing,”TheEuropeanPhysicalJournalA,vol.59,no.94(May2023),p.1,at

/10.1140/epja/s10050

-023-01006-7.

8Microsoft,ExploreQuantum:TypesofQubits,AzureQuantum,at

/en

-us/explore/concepts/types-of-qubits.

9SeeMicrosoft,ExploreQuantum:Superposition,AzureQuantum,at

/en

-us/explore/concepts/superposition.

10Microsoft,ExploreQuantum:Entanglement,AzureQuantum,at

/en

-us/explore/concepts/entanglement.

11Microsoft,ExploreQuantum:TheQubit,AzureQuantum,at

/en

-us/explore/concepts/what-is-a-qubit.SeealsoCaliforniaInstituteofTechnology(Caltech),WhatIsQuantumComputing?,CaltechScienceExchangeSeries:QuantumScienceandTechnology,at

/topics/quantum

-science-

explained/quantum-computing-computers.

12IBM,WhatIsQuantumComputing?,at

/topics/quantum

-computing.

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development).13However,therearepracticalimplementationchallengessuchasmaintainingaqubit’ssuperpositionandcorrectingcalculationerrors(discussedinthefollowingsub-section,

“IncreasingQuantumComputingReliability”

),leadingtouncertaintyaboutwhetherandwhenquantumcomputingcouldbebroadlydeployedandapplied.

TheCurrentStateofQuantumComputing

SincetheenactmentoftheNQIActin2018,researchershavemadenotableadvancesinquantumcomputinginthreespecificareas.

DemonstratingQuantumAdvantage

InOctober2019,aresearchteamledbyscientistsfromGoogle’squantumgroupreportedthataquantumprocessorwith54qubitstookabout200secondstocompleteaspeciallydesigned

computation;anequivalentcomputationwouldtakeastate-of-the-artclassicalsupercomputerapproximately10,000years.Theresearchersclaimedthattheirexperimentdemonstrateda

milestoneforquantumcomputing—thefirstcomputationaltaskexecutedmuchfasterona

quantumprocessorthanonaclassicalprocessor.Thisachievementalsodemonstratedso-called“quantumadvantage”or“quantumspeedup”overclassicalcomputing.

InApril2023,anotherresearchteamledbythesameGooglegroupreportedthatasecond

generationofitsquantumprocessor,with70qubits,performedamorecomplextaskthantheonereportedin2019.Accordingtotheresearchers’estimate,thesametaskwouldtakeabout47years

fortheFrontiersupercomputeratOakRidgeNationalLaboratory—thefastestclassical

computingsystemintheworldatthetime.14Theresearchersclaimedthatsuchacomputationaltaskwasbeyondthecapabilitiesofmanyexistingclassicalsupercomputers.15

Despitethesesuccesses,someexpertsarguethatresearchershavethusfaronlydemonstratedquantumadvantageoverclassicalcomputersinsolvingmathematicalproofsandthatquantumadvantagemaynothavepracticalvaluebeyondacademicresearch.16

IncreasingQuantumComputingReliability

Tomakequantumcomputingbroadlyapplicableinsolvingpracticalproblems,researchershaverecognizedtheneedfortechnicaladvancestoincreasethereliabilityofquantumcomputers.17

Manyresearchersagreethatamajoroutstandingchallengetoquantumcomputingis“noise,”

13MichaelBrooks,“QuantumComputers:WhatAreTheyGoodFor?,”Nature,vol.617(May2023),pp.S1-S3,at

/10.1038/d41586

-023-01692-9.

14AlexisMorvanetal.,“PhaseTransitioninRandomCircuitSampling,”arXiv,2304.11119(April2023),p.5,at

/10.48550/arXiv.2304.11119

.FrontierremainedthefastestclassicalcomputingsystemintheworldasofJune2023.SeeTop500,“TOP500,”61stedition,June2023,at

/lists/top500/2023/06/

.

15AlexisMorvanetal.,“PhaseTransitioninRandomCircuitSampling,”arXiv,2304.11119(April2023),p.1,at

/10.48550/arXiv.2304.11119

.

16MichaelBrooks,“QuantumComputers:WhatAreTheyGoodFor?,”Nature,vol.617(May2023),pp.S1-S3,at

/10.1038/d41586

-023-01692-9.SeealsoMattSwayne,“GoogleClaimsLatestQuantumExperiment

WouldTakeDecadesonClassicalComputer,”TheQuantumInsider,July4,2023,at

/

2023/07/04/google-claims-latest-quantum-experiment-would-take-decades-on-classical-computer/.

17FrankAruteetal.,“QuantumSupremacyUsingaProgrammableSuperconductingProcessor,”Nature,vol.574(October2019),pp.505–510,at

/10.1038/s41586

-019-1666-5.

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whichcanaffecttheaccuracyofcalculationsmadebyaquantumcomputer.18Noisereferstoanydisturbancetoaqubit’senvironment,suchasheat,light,thermalvibrations,electromagnetic

radiation,Earth’smagneticfield,cosmicrays,orneighboringqubits,amongothers.19Qubitsarehighlysusceptibletonoise,whichcancausethelossofinformationitholds.20Errorratesare

generallyhigherinquantumcomputersthaninclassicalcomputers.21

Noiseintroduceserrorsinquantumcalculationsthataredifficulttocorrect22andlimitsthe

numberofqubitsaquantumcomputercanhave.23Solutionstothischallengeincludedevelopingfault-tolerantquantumprocessorsorrunningfullyerror-correctedquantumalgorithms.Both

approachesrequireatleasttensofthousandsofqubits,24wellbeyondthecapacityofcurrentquantumprocessors.25

Somepromisingrecentresearchresultspointtothepossibledevelopmentoftechniquesthatmayhelpreduceerrorandincreasereliability.InJune2023,ateamledbyIBMquantumresearchers

presentedtheresultsofanexperimentto“controllablymanipulate”quantumnoise,demonstratingsuccessinanexperimentalsetting.26Google’squantumresearchgroupreportedinFebruary2023thatitsresearcherswereabletodemonstratethatincreasingthenumberofqubitscanlowerthe

errorrateofcalculationsinaquantumcomputer.27Theresearchersadmittedthattheimprovementontheerrorrateintheirexperimentwasstillsmall,anderrorratesneedstodropmuchmoreto

realizethepotentialofsolvingproblemsbeyondthereachofclassicalcomputers.28Someexpertsarguethatprogresssofarhasmitigated,butnotfullycorrected,calculationerrors,andonlyfullquantumerrorcorrectioncantrulyenablereliablequantumcomputing.29

18YoungseokKimetal.,“EvidencefortheUtilityofQuantumComputingBeforeFaultTolerance,”Nature,vol.618(June2023),pp.500–505,at

/10.1038/s41586

-023-06096-3.

19JuanMoreno,GrantSalton,andTimChen,NoiseinQuantumComputing,AWSQuantumTechnologiesBlog,September8,2022,at

/blogs/quantum

-computing/noise-in-quantum-computing/.SeealsoAdamZewe,ATechniqueforMakingQuantumComputingMoreResilienttoNoise,WhichBoostsPerformance,ScienceX,March22,2022,at

/news/2022

-03-technique-quantum-resilient-noise-boosts.html.

20AdrianCho,“NoRoomforError,”Science,July9,2020,at

/content/article/biggest

-flipping-challenge-quantum-computing.

21AdamZewe,ATechniqueforMakingQuantumComputingMoreResilienttoNoise,WhichBoostsPerformance,ScienceX,March22,2022,at

/news/2022

-03-technique-quantum-resilient-noise-boosts.html.

22DavidCastelvecchi,“IBMQuantumComputerPassesCalculationMilestone,”Nature,vol.618(June2023),pp.656-657,at

/10.1038/d41586

-023-01965-3.

23MichaelBrooks,“BeyondQuantumSupremacy:TheHuntforUsefulQuantumComputers,”Nature,vol.574(October2019),pp.19-21,at

/10.1038/d41586

-019-02936-3.

24DavidCastelvecchi,“IBMQuantumComputerPassesCalculationMilestone,”Nature,vol.618(June2023),pp.656-657,at

/10.1038/d41586

-023-01965-3.

25YoungseokKimetal.,“EvidencefortheUtilityofQuantumComputingBeforeFaultTolerance,”Nature,vol.618(June2023),pp.500–505,at

/10.1038/s41586

-023-06096-3.

26Ibid.

27GoogleQuantumAI,“SuppressingQuantumErrorsbyScalingaSurfaceCodeLogicalQubit,”Nature,vol.614(February2023),pp.676-681,at

/10.1038/s41586

-022-05434-1.

28DavideCastelvecchi,“Google’sQuantumComputerHitsKeyMilestonebyReducingErrors,”Nature,February22,2023,at

/10.1038/d41586

-023-00536-w.

29DavidCastelvecchi,“IBMQuantumComputerPassesCalculationMilestone,”Nature,vol.618(June2023),pp.656-657,at

/10.1038/d41586

-023-01965-3.

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AchievingQuantumAdvantageforPracticalProblems

Someexpertshavesuggestedfocusingonthedevelopmentofquantumcomputersthatprovidepracticalquantumadvantage,beyondsimulatingandtestingquantumhardware.30Practical

quantumadvantagemeansusingquantumcomputerstoreliablytackleuseful,real-worldproblemsthatleadingclassicalsupercomputerscannotaddress.Itwillrequirealarge-scale

quantumcomputerwiththousands,hundredsofthousands,orevenmillionsofqubits,depending

onfactorssuchasthetypeofproblem,thealgorithm,andthearchitectureofthequantumhardware.31Quantumprocessorsatthisscaledonotyetexist.

Toachievepracticalquantumadvantage,leadingindustryplayershavesettheirR&Droadmapstoscaleupquantumprocessorswithqubits.InNovember2022,IBMannounceda433-qubit

processorbasedonsuperconductingtechnology.32Thecompanyclaimedthatitwasontracktodelivera1,000-qubitprocessorbytheendof2023.33InMay2023,IBMlauncheda$100millionpartnershipwiththeUniversityofTokyoandtheUniversityofChicago,aimingtodevelopa

quantumsupercomputerby2033poweredby100,000qubits,34whichitpredictswillallowthesupercomputertoperformsomeusefultaskswithpracticalquantumadvantage.35

ResearchersatGooglebelievethatscalingupqubitsalsohelpstoimprovequantumerror

correction—therequiredfeatureofgeneral-purposequantumcomputers.36Googleisreportedlyworkingtowarda1,000-qubitprocessorandexpectstoachievethismilestoneasearlyas2025.37Ithopestodemonstrateauseful,error-correctedquantumcomputerwithonemillionqubits

withinadecade.38

30AndrewJ.Daleyetal.,“PracticalQuantumAdvantageinQuantumSimulation,”Nature,vol.607(July2022),pp.667-676,at

/10.1038/s41586

-022-04940-6.SeealsoJohnPreskill,“QuantumComputingintheNISQEraandBeyond,”Quantum,vol.2(July2018),pp.79-99,at

/10.22331/q

-2018-08-06-79.

31JohnPreskill,“QuantumComputingintheNISQEraandBeyond,”Quantum,vol.2(July2018),pp.79-99,at

/10.22331/q

-2018-08-06-79;MichaelE.Beverlandetal.,“AssessingRequirementstoScaletoPracticalQuantumAdvantage,”arXiv,2211.07629(November2022),at

/10.48550/arXiv.2211.07629

;Craig

GidneyandMartinEker?,“HowtoFactor2048BitRSAIntegersin8HoursUsing20MillionNoisyQubits,”

Quantum,vol.5(April2021),pp.433-464,at

/10.22331/q

-2021-04-15-433;andGoogle,“OurFocused

andResponsibleApproachtoQuantumComputing,”at

https://ai.google/static/documents/approach

-quantum-computing.pdf.

32IBM,“IBMUnveils400Qubit-PlusQuantumProcessorandNext-GenerationIBMQuantumSystemTwo,”

November9,2022,at

/2022

-11-09-IBM-Unveils-400-Qubit-Plus-Quantum-Processor-and-Next-Generation-IBM-Quantum-System-Two.

33IBM,“TheIBMQuantumDevelopmentRoadmap,”2022,at

/quantum/roadmap

.

34IBM,“IBMLaunches$100MillionPartnershipwithGlobalUniversitiestoDevelopNovelTechnologiesTowardsa100,000-QubitQuantum-CentricSupercomputer,”May21,2023,at

/2023

-05-21-IBM-

Launches-100-Million-Partnership-with-Global-Universities-to-Develop-Novel-Technologies-Towards-a-100,000-Qubit-Quantum-Centric-Supercomputer.

35JayGambettaandMatthiasSteffen,“ChartingtheCourseto100,000Qubits,”IBMResearchBlog,May21,2023,at

/blog/100k

-qubit-supercomputer.

36GoogleQuantumAI,“SuppressingQuantumErrorsbyScalingaSurfaceCodeLogicalQubit,”Nature,vol.614

(February2023),pp.676-681,at

/10.1038/s41586

-022-05434-1.SeealsoSankarDasSarma,“QuantumComputingHasaHypeProblem,”MITTechnologyReview,March28,2022,at

/

2022/03/28/1048355/quantum-computing-has-a-hype-problem/.

37Google,“OurFocusedandResponsibleApproachtoQuantumComputing,”at

https://ai.google/static/documents/

approach-quantum-computing.p