Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits

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1、Completeuniversalquantumgatesetapproachingfault-tolerantthresholdswithsuperconductingqubitsJerryM.Chow,1JayM.Gambetta,1A.D.C´orcoles,1SethT.Merkel,1JohnA.Smolin,1ChadRigetti,1S.Poletto,1GeorgeA.Keefe,1MaryB.Rothwell,1J.R.Rozen,1MarkB.Ketchen,1andM.Steffen11

2、IBMT.J.WatsonResearchCenter,YorktownHeights,NY10598,USA(Dated:February27,2012)Weusequantumprocesstomographytocharacterizeafulluniversalsetofall-microwavegatesontwosuperconductingsingle-frequencysingle-junctiontransmonqubits.Allextractedgatefidelities,includ

3、ingthoseforCliffordgroupgenerators,single-qubitπ/4andπ/8rotations,andatwo-qubitcontrolled-NOT,exceed95%(98%),without(with)accountingforstatepreparationandmeasure-menterrors.Furthermore,weintroduceaprocessmaprepresentationinthePaulibasiswhichisvisuallyefficien

4、tandinformative.Thishigh-fidelitygatesetservesasanothercriticalbuildingblocktowardsscalablearchitecturesofsuperconductingqubitsforerrorcorrectionschemes.PACSnumbers:03.67.Ac,42.50.Pq,85.25.-jAcriticalprerequisiteforbuildingascalablefault-resonance(CR)intera

5、ction[9,15,16].Althoughthegatetolerantquantumcomputeristheapplicationoferrorfidelitiesareobtainedviastandardquantumprocessto-correctioncodes[1–3].Inordertoemploythesecodes,mography(QPT)ofeachrespectivegate,inthisworkwetheunderlyingquantumgatesmustbeperforme

6、dwithintroduceadifferent,butefficientvisualrepresentationhighfidelityabovecertainthresholdlevels.Experimen-ofprocessmaps,thePaulitransfermatrix,R.Rde-tally,theonuscurrentlyliesinmakingscalablephysicalscribestheactionofaprocessonthecomponentsofthesystemswithuni

7、versalquantumgatesetswhichsurpassdensitymatrixrepresentedinthebasisofPaulioperatorsthesethresholds.andhelpsestablishanumberofpropertiesoftheunder-lyingprocesswhichareotherwisehiddeninthestandardTwo-dimensionalerror-correctionsurfacecodes,withchi-matrixrepr

8、esentation[14].Wefindslightvariationsgatefidelitythresholdsof∼90-99.5%dependingonmea-inthefidelitiesacrossthedifferentgatesand,fromthesurementerrors[2–4],areparticularlywell-suitedforsu-associatedmaps,identifytha