complex networks from classical to quantum jacob biamonte资料.pdf

该【complex networks from classical to quantum jacob biamonte资料 】是由【dt83088549】上传分享，文档一共【10】页，该文档可以免费在线阅读，需要了解更多关于【complex networks from classical to quantum jacob biamonte资料 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。REVIEWARTICLEhttps:///-019-0152-6OPENworksfromclassicaltoquantumJacobBiamonte1,in2&ManlioDeDomenico3worktheorytoproblemsinquantuminformationhas1234567890():,;resultedinabene?cialcross-essfullybeenappliedtotransportandentanglementmodelswhileinformationphysicsissettingthestageforaplexsystemswithquantuminformation-—whereedgesrepresententangledlinks—,pinpointingthesimilaritiesandthedifferencesfoundattheintersectionofthesetwo?,chemistry2,andmachinelearning3andtoofferquantumsecurityenhancementQ45munications,.Rapidexperimentalpro-municationdevicesintotrulydata-intensivedomains,plexfeatures,givingrisetowhatappearsasaparadigmshiftneededtofaceafundamentaltypeofcomplexity6–—traditionallybasedonstatisticalmechanics—,worktheoryhasdemonstratedthatmany(non-quantum)plexfeatures14–18,intheorganizationoftheirstructureanddynamics19–24,thecontrollabilityoftheirconstituents25,andtheirresiliencetostructuralanddynamicalperturbations26–,aswellasnovelplexfeaturesinquantumsystems6–12,?rstconsistsofquantumsystemswhoseconnectionsarerepresentedbyentangledstates6,33,,suchasatomsorsuperconductingquantumelectronics,whoseconnectionsarephysical35–-enhancedalgorithmsorquantuminformationtransportsystems,,thetwotypesof1DeepQuantumLabs,SkolkovoInstituteofScienceandTechnology,3NobelStreet,Moscow143026,,UniversitéCatholiquedeLouvain,EulerBuilding4,AvenueLemaitre,B-1348Louvain-la-Neuve,,FondazioneBrunoKessler,ViaSommarive18,38123Povo,TN,.(email:@).(email:mauro.******@).(email:******@)COMMUNICATIONSPHYSICS|(2019)2:53|https:///-019-0152-6|msphys1MUNICATIONSPHYSICS|https:///-019-0152-6Box1:Cross-worksandquantuminformationscienceInrecentyears,(currentstatus)GraphityandQuantumtransportemergentmodelsworksQuantumwalkssolvinggraphrecognitionofspace-timeworkmodelsandsearchenginerankingproblemsWalkmodelsofexcitontransportplexesmunicationworksRandomquantumcircuitsQuantumgeneralizationsofrandomgraphmodelsworksEachoftheshadedregionsrepresentpublished?ndingsthatmapoutthe?eldfromtheoretical,experimental,—bothcoveredinthisreview—aswellasthequantumalgorithmsdevelopedtoaddress-?cationinthebottomareaincludesquantumnetworksbasedonentangledstatesandonphysicalconnections—alsocoveredinthisreview—workmodelsofspace-time,randomquantumcircuits,works,andgeometryworksaredescribedbyquantuminformationtheory,workscience,worksexhibitwhatisworkdescriptors—plexity”.Here,wewillrecallbrie?ythebasicsuchasrankingindicators,similarity,andcorrelationmeasures—,thesametoolscanthenbeappropriatelymod-,workisanabstractrepresentationofrelationshipsworkinformationtheory—suitable(encodedbyedges)betweenunits(encodedbynodes),.,theycanrepresentsystems32,41,-ingtooroutgoingfromanodeand,ingeneral,,thesetwo?elds().Severalquantumeffectsarestilloutgoing,ing,outgoing,and-totaldegreeofanode,,outgoing,andtotalstrengthofthatworks,whichnode,,?edpathforwardappearstobethroughthedistributionareknownasErdos–works,whereassys--lawdegreedistributionareknownasscale-freeHere,,,wedonotcoverseveraltopicsthat,worktheorycanbenevertheless,deservetobementionedaspartofthe?,worksareinclude,innoparticularorder,(i)works43–46,synchronizationinandonquantumQuantumspinsarrangedongraphs;(ii)quantumrandomwalksnetworks47,quantumrandomcircuits48,49,classicalspinmodels,ongraphs;(iii)works;(iv)Superconductingworkquantum(electrical)circuits;(v)workstates;(vi)theory50–52().Quantumgraphstates,etc.-workisnotde?nedinastrictsense,thede?nitionistypicallythatworkthatexhibitsanemergentproperty,suchasanon-,workreasoning2COMMUNICATIONSPHYSICS|(2019)2:53|https:///-019-0152-6|msphysCOMMUNICATIONSPHYSICS|https:///-019-0152-,wewillfocusontopicsinquantumsystemsthatareknowntobe-,letusABSstartfromthestateofeachithqubit,writtenwithoutlossofgenerality,asψαàiiα;i?|0?and|1?putational”,workedge34isinapure,coherentsuperpositionofthetwobasisstatesandanymeasurementinthissamebasiswillcausethestatetocollapse??2α2α––onto|0or|1,withprobabilitycos(i)andsin(I),,whichexhibitsnon-Letusconsideraquantumsystemwithtwoqubits,.,i=,tensorpro-obtain,withprobabilityapproachingunity,aquantumstatewithduct,ofthetwobasisstates:|00?,|01?,|10?,and|11?.Ifthetwothetopologyofany?nitesubgraphforNapproachingin?nityqubitsarenotentangled,.,theirstatesareindependentfromandz=?,worktheoryandquantumψ?=ψ??ψ?.,|12|1|2,whereasthisisnotpossibleifthetwotheoryprovidesapowerfultooltoinvestigatethecriticalprop-,inthecaseofregularcaseofmixedstatesisobtainedintermsofthenon-negativelattices,ithasbeenshownthattheprobabilitypopttoestablishadensitymatrixρ;aunittraceHermitianoperatorrepresentingtheperfectquantumchannelbetweenthenodescanbemappedtothestateofthesystemasanensembleof(unknown),suchaslattice6,ascenariothatcanbestudiedusingthewell-establisheduniformlatticestypicallystudiedincondensedmatterphysics,itbond--onetocalculatethecriticalprobabilityabovewhichthesystemwillglementbetweentwonodesinsuchawaythatitequalstheexhibitanin?niteconnectedclusterand,inthecaseofqubits,itprobabilitytohavealinkin(classical)Erdos–(N,p),within?nitelength—.,anin?nitesequenceofentangledstateswhereNisthenumberofnodesandptheprobabilityto?ndaconnectinganin?nitenumberofqubits—,,denotingtheexistenceofaworkfollowingapowerlawp∝N?z,withz≥,localworktheory,thereexistsacriticalvalueforthemeasurementsbasedonthisapproach,calledclassicalentangle-probabilitypc(N)forwhich,ifp>pc(N)agivensubgraphofnmentpercolation(CEP),arenotoptimal,ingeneral,:CEPisnotevenasymptoticallyopti-classicalresultisthatthiscriticalprobabilityscaleswithNasmalfortwo-dimensionallatticesandnewquantumprotocols?n/lpc(N)∝,Cirac,,de?ninganentanglementofthispicturetothequantumrealmbyreplacingeachlinkwithphasetransition,emergesfromthisnewstrategy,wherethecritical=anentangledpairofparticles,wheretheprobabilitypi,jpthatparameteristhedegreeofentanglementrequiredtobedistributedthelinkexistsbetweennodesiandjissubstitutedbyaquantuminordertoestablishaquantumchannelwithprobabilitythatdoesρ=ρstatei,j:oftwoqubits,oneateachnode().Onecannotdecayexponentiallywiththesizeofthesystem,atvarianceworkwhereeachnodeconsistsofN?,whichareentangled,inpairs,,suchasHowever,inthiscase,althoughtheconnectionsareidenticalandErdos–Renyi,scale-free,andsmall--=|????|,àáp???????????p???ji??p???2àpjit00pji11:e2Tconnectivityandnotthehubs,breakingdowntheusualhier-,,Here,0≤p≤1quanti?estheentanglementoflinksandthenamednon-bilocal,correlatingdistantqubitsbymeansofseveralstateoftheoverallquantumrandomgraphcanbedenotedby|Gintermediate,typicallyindependent,sources,andprovidingevi-(N,p)?.Ifeachlink,.,eachentangledpair,(p=1/2)throughlocalworkconnectivitymunication(),theoptimaldescribedhere,,.,workconceptshavefoundapplic-criticalprobabilityscaleswithsystemsize,itispossibletocontrolabilityconsistsofquantumsystemsphysicallyinterconnected,worksuchasatomsorsuperconductingquantumelectronics35–,suchThesetypesofsystemsprovidefertilegroundwherequantumCOMMUNICATIONSPHYSICS|(2019)2:53|https:///-019-0152-6|msphys3MUNICATIONSPHYSICS|https:///-019-0152-6algorithmsaretested58–62andquantuminformationtransporteigenvaluecorrespondingtoaneigenvectorofpositiveentriesGp=systemsarestudied63–“quantumwalks”works,upationprobabilitiesofarandomwebsurfer—itrepresentsastudiesshowingthatquantuminformationtasks,,retainperformanceinverydis-ThevectorpisknownasthePage-(non-quantum)putationinorderworktheory—–--particlequantumwalksrepresentauniversalconsiderquantumversionsofGoogle’sPage-Rank8–-putation—-work,whereasBurillograph—and,inaddition,,in