基于超导量子比特网络的Deutsch-Jozsa算法实现方案

ImplementingDeutsch-JozsaalgorithmusingsuperconductingqubitnetworkXiao-HuZheng¤,1MingYang,1PingDong,1andZhuo-LiangCaoy11KeyLaboratoryofOpto-electronicInformationAcquisitionandManipulation,MinistryofEducation,SchoolofPhysicsandMaterialScience,AnhuiUniversity,Hefei,230039,PRChinaAnimprovedarchitecture,whichperformauniversalsetofgatesbycurrentbiasingofcouplingJosephsonjunction,hasbeenproposed.Thisimprovementisnecessarytotherealizationofafunctionalandscalablequan-tumcomputer.Theproposedarchitectureisinlinewithcurrenttechnology.Secondly,weinvestigateaschemeforimplementingDeutsch-Jozsaalgorithmviatheimprovedarchitecture.Itisasimple,scalableandfeasi-bleschemefortheimplementationofDeutsch-Jozsaalgorithmbasedonthecurrent-controlledsuperconducingchargequbitnetwork.PACSnumbers:03.67.Lx,85.25.CpKeywords:Deutsch-Jozsaalgorithm;Superconduction;JosephsonchargequbitsSuperpositionprincipleofquantumstateandentanglementpropertymakequantumcomputerspossesspotentiallysupe-riorcomputingpowerovertheirclassicalcounterparts,whichisdemonstratedbysomeQuantumalgorithms.Shor’sal-gorithm[1]canbeusedtoquicklyfactorizelargenumbers.GroversearchalgorithmisfairlyefficientinlookingforoneiteminanunsorteddatabaseofsizeN´2n[2,3].TheDeutsch-Jozsa(DJ)algorithm[4]isoneofthesimplequan-tumalgorithmwhichprovidesanexponentialspeed-upwithrespecttoclassicalalgorithms.Inthispaper,wefocustheDJalgorithm.TheDJalgorithmcanbebrieflydescribedasfollows:As-sumeaBooleanfunctionsf:f0;1gN!f0;1g.Ifthefunc-tionvaluesareonlysingle0or1forall2Ninputs,thefunc-tioniscalledconstant.Ifthefunctionvaluesareequalto1forhalfofallpossibleinputs,andto0fortheotherhalf,thefunctioniscalledbalanced.TheDJalgorithmisdesignedtodistinguishwhetherafunctionfisconstantorbalanced.Withaclassicalalgorithm,thisproblemwould,intheworstcase,require(2N¡1+1)queriesoffwhereastheDJalgorithmre-quiresonlyonequerybymeansofthefollowingsteps[5,6],asshownFig.1(hereweeliminatea1-qubitfunctionregisterwhichisusedforstoringthefunctionvalues,whileretainanN-qubitcontrolregisterforthefunctionarguments).(i)Nqubitsarepreparedintheinitialstatej00:::0i.(ii)PerformanN-qubitHadamardtransformationH(iii)Applythef-controlledphaseshiftUfjxiUf¡!(¡1)f(x)jxi;(x2f0;1gN):(1)(iv)PerformanotherHadamardtransformationH.(v)Measurethefinalstate.Iftheresultisj00:::0ithefunctionfisconstant;if,however,theamplitudeaj00:::0iofthestatej00:::0iiszerothefunctionfisbalanced.Thisisbecauseaj00:::0i=12NXx2f0;1gN(¡1)f(x):(2)¤Electronicaddress:[e-mail]:[e-mail](CorrespondingAuthor)measurefinalstateprepareInitialstatefUHHFIG.1:SchematicdiagramoftheDeutsch-JozsaForrealizingquantumcomputers,somephysicalsystems,suchasnuclearmagneticresonance[7],trappedirons[8],cavityquantumelectrodynamics(QED)[9],andopticalsys-tems[10]havebeenproposed.Thesesystemshavethead-vantageofhighquantumcoherence,butcan’tbeintegratedeasilytoformlarge-scalecircuits.Becauseoflarge-scalein-tegrationandrelativelyhighquantumcoherence,Josephsonchargequbit[11–13]andfluxqubit[14,15],whicharebasedonthemacroscopicquantumeffectsinsuperconductingcir-cuits[16,17],arethepromisingcandidatesforquantumcom-puting.TheDJalgorithmhasspecialfunctions,sotheimple-mentationofDJalgorithmhasbecomethefocusofresearch.Forexample,theDJalgorithmhasbeenimplementedwithpurecoherentmolecularsuperpositions[18],withquantumdot[19,20],andwithcavityQED[21].Inthispaper,wepro-poseaphysicalschemeforimplementingtheDJalgorithmwithsuperconductingqubitnetwork.Itisasimple,scalableandfeasibleschemeforimplementingtheDJalgorithm.Thepaperisorganizedasfollows:Firstly,weintroducethestructureandHamiltonianofthecurrent-controlledsu-perconducingchargequbitnetwork.Secondly,weexplainhowtoimplementauniversalsetofgateswiththisnetwork.Thirdly,wereviewtheadvantages,thedecoherencefeatureandextendabilityofthesuperconductingchargequbitnet-work.Fourthly,weillustratetheimplementationoftheDJalgorithm.Finally,theconclusionsaregiven.SincetheearliestJosephsonchargequbitscheme[11]wasproposed,aseriesofimprovedschemes[12,22,23]havebeenexplored.Here,basingonthearchitectureofJoseph-sonchargequbitinRef.[23],weproposeanimprovedarchitecture.ThesuperconductingchargequbitsstructureisshowninFig.2.AllNchargequbits(Q1;Q2;:::;QN)caninteractwiththechargequbitQ0byacommonlarge-)…LNBIRNBIgNVNQ2Q1Q0QFIG.2:Acurrent-controlledsuperconductingchargequbitnetworkstructure.AllNchargequbits(Q1;Q2;:::;QN)caninteractwiththechargequbitQ0byacommonlarge-capacitanceJosephsonjunc-tion(JJ)(denotedasacrossedrectangle).Eachcharge-qubitQk(k=0;1;2;:::;N)iscontrolledbyavoltageVgkandalo-calmagneticflux©Xk,whereasthecouplingofthetwoqubitsisadjustedbythebiascurrentIb.capacitanceJosephsonjunction(JJ)(denotedasacrossedrectangle).Forthekthcharge-qubit,asuperconductingislandwithchargeQk=CkVgk=2enkisweaklycoupledbytwosymmetricdirectcurrentsuperconductingquantuminterfer-encedevices(dcSQUIDs)andbiasedbyanappliedvoltagethroughagatecapacitanceCk.Assumethatthetwosym-metricdcSQUIDsareidenticalandallJosephsonjunctionsinthemhaveJosephsonc