《智能信息處理與量子計算》全套教學(xué)課件

Quantum

Intelligence

Computing《智能信息處理與量子計算》第1講全套可編輯PPT課件2024/8/2212017年9月29日，中國一顆名為“墨子號”的衛(wèi)星使維也納和北京這兩個相隔半個地球的城市之間的視頻會議成為可能。當(dāng)它以每小時18,000英里(29,000公里)的速度劃過夜空時，衛(wèi)星向位于興隆的一個地面站發(fā)射了一個小數(shù)據(jù)包。不到一個小時后，衛(wèi)星經(jīng)過奧地利，將另一個數(shù)據(jù)包發(fā)送到格拉茨市附近的一個站。這些包是保護數(shù)據(jù)傳輸安全的加密密鑰，而且是量子密鑰。世界上第一個量子加密的洲際視頻鏈接。2024/8/2222024/8/2232024/8/224量子信息學(xué)，是量子力學(xué)與信息科學(xué)相結(jié)合的產(chǎn)物，是以量子力學(xué)的態(tài)疊加原理為基礎(chǔ)，研究信息處理的一門新興前沿科學(xué)量子信息學(xué)包括量子密碼術(shù)、量子通信、量子計算機等幾個方面2024/8/225In

physics

and

computerscience,

quantuminformation

isphysicalinformation

thatisheldinthe

state

ofaquantumsystem.Quantuminformationisthebasicentitythatisstudiedintheburgeoningfieldof

quantuminformationtheory,andmanipulatedusingtheengineeringtechniquesof

quantuminformationprocessing.Muchlikeclassicalinformationcanbeprocessedwith

digitalcomputers,

transmitted

fromplacetoplace,manipulatedwith

algorithms,andanalyzedwiththe

mathematics

ofcomputerscience,soalsoanalogousconceptsapplytoquantuminformation.2024/8/226‘IthinkIcansafelysaythatnooneunderstandsquantumphysics’2024/8/227saidbyRichardPhillipsFeynman,thepioneerofquantumcomputing,thewinnerofNobelPrizeinPhysics,19651982年，美國著名物理物學(xué)家理查德·費曼在一個公開的演講中提出利用量子體系實現(xiàn)通用計算的新奇想法——如果用量子系統(tǒng)所構(gòu)成的計算機來模擬量子現(xiàn)象則運算時間可大幅度減少，從而量子計算機的概念誕生了。WhyQuantumComputers?QuantumIntelligenceComputingHowQuantumComputerswouldWork?Outline3212024/8/22

Integerprimefactorization921=3×7221=13×17221=?11021=?11021=103×107SeveralμsWhyQuantumComputer

Largeprimefactorization232digitsnumber(768bits)?1230186684530117755130494958384962720772853569595334792197322452151726400507263657518745202199786469389956474942774063845925192557326303453731548268507917026122142913461670429214311602221240479274737794080665351419597459856902143413=33478071698956898786044169848212690817704794983713768568912431388982883793878002287614711652531743087737814467999489×36746043666799590428244633799627952632279158164343087642676032283815739666511279233373417143396810270092798736308917WhyQuantumComputer

2024/8/2210

Largeprimefactorization232digitsnumber(768bits)Thecomputationtook6monthson802.2

GHzcomputers[T.Kleinjung10]Aquantumcomputer?Ifonasinglecore2.2GHzprocessorwith2GBRAM,1500yearsThefactorizationofthe768-bitnumberwouldbeamatterofseconds[T.Phillips10]WhyQuantumComputer

2024/8/2211

LargeprimefactorizationCryptographyschemeswidelyusedine-businessisbasedontheassumptionthatfactoringlargenumbersiscomputationallyinfeasibleWhyQuantumComputer

QuantumComputeramatterofseconds

Internetwillnotbesafe2024/8/2212designapracticalcryptosystemwithcredibleevidenceofsecurityagainstquantumattackQuantumCryptographyChallengeWeneedQuantumComputer2024/8/2213WhyQuantumComputers?QuantumIntelligenceComputingHowQuantumComputerswouldWork?Outline321HowQuantumComputerswouldwork2024/8/2215量子計算機是一類遵循量子力學(xué)規(guī)律進行高速數(shù)學(xué)和邏輯運算、存儲及處理量子信息的物理裝置當(dāng)某個裝置處理和計算的是量子信息，運行的是量子算法時，它就是量子計算機QuantumComputer

DataRepresentationHowQuantumComputerswouldwork2024/8/2216

Measurement

DataProcessing

DataRepresentationState:onoroffBit:0or1AnelectronHowQuantumComputerswouldwork2024/8/2217electroncloudinahydrogenatom2024/8/2218

DataRepresentationSuchasuperposition,isthebasicunitofencodedinformationinquantumcomputersHowQuantumComputerswouldwork2024/8/2219Quantumbit(qubit)AQubit(Quantumbit)canberepresentedas

whereα0andα1

arecomplexnumbers

|α0|2+|α1|2=1AQubitmaybeinthe“1”state,inthe“0”state,orin

anylinearsuperposition

ofthetwoHowQuantumComputerswouldwork2024/8/2220Forexample,3qubits

Multi-qubitsisalinearsuperpositionofthe8

classicalstates{|000>,|001>,|010>,|011>,|100>,|101>,|110>,|111>}HowQuantumComputerswouldwork2024/8/2221

nqubits

Multi-qubitsisalinearsuperpositionoftheN=2nclassicalstatesHowQuantumComputerswouldworkSo,itcanrepresentN=2n

numbersatthesametime2024/8/2222

MeasurementForcingthesystemtodecideonaparticularstate,withprobabilitiesdeterminedbytheamplitudesHowQuantumComputerswouldwork2024/8/2223

DataProcessingTransformationUfisanUnitaryOperatorHowQuantumComputerswouldwork2024/8/2224H:CircuitsS:Algorithms

QuantumParallelismTransformationUfisappliedtoallN=2n

basisstatessimultaneouslyasuperpositionofallN=2nbasisstates

HowQuantumComputerswouldwork2024/8/2225

QuantumgateX–negation,NOTgateY=ZX,PauligateZ-phaseshiftgateI-identitytransformationPerform

UnitaryOperationHowQuantumComputerswouldwork2024/8/2226HowQuantumComputerswouldwork

QuantumgateControlled-NOTgateHadamardgatereversible2024/8/2227HowQuantumComputerswouldwork

QuantumgateArrayCanperformallquantumcomputationsreversibleA128qubitprocessorchipsetconstructedbyD-WaveSystemsInc.,in20112024/8/2228HowQuantumComputerswouldwork

QuantumAlgorithmsreversible2024/8/2229QuantumIntelligenceComputingWhyQuantumComputers?QuantumIntelligenceComputingHowQuantumComputerswouldWork?Outline321QuantumIntelligenceComputing

QuantumNeuralNetworks2024/8/2231

QuantumGeneticAlgorithm

QuantumSearchAlgorithm

QuantumSwarm

IntelligenceAlgorithmsearchanamefrom10,000entriesinanunsorted

telephonedirectoryclassicalalgorithmcanbeestimatedattaking5,000

steps()Grover’squantumsearchalgorithmwouldtakeonly100steps!()2024/8/2232Grover’sQuantumSearchAlgorithmMechanismofGAreadtheresultInitializationPrepareann-QubitGroverIteration

SelectiveInversion

InversionaboutAverage

TerminationconditionMeasurementYesNoGrover’sQuantumSearchAlgorithm2024/8/2233MechanismofGASimulationofGrover’sAlgorithminaclassicalComputerGrover’sQuantumSearchAlgorithm2024/8/2234QuantumIntelligenceComputinginSignalProcessingQuantumSearchAlgorithmforLarge-ScaleImageRetrieval

QuantumAlgorithms

for

CommunicationSignalDetection

QuantumAlgorithms

forMachineRecognitionofHumanFaces2024/8/2235HowdifficultandHowfar?/watch?v=VyX8E4KUkWw/watch?v=JcW9YGdoKxo&feature=related2024/8/22362024/8/2237newandgreatideasinsignalprocessingQuantumIntelligenceComputingItmaygiveusItisengaging!AboutCourse38ThankYouforyourattention!Q&AGrover’sQuantum

SearchAlgorithmanditsApplication《智能信息處理與量子計算》第2講Motivation:

QCGA

BasedSignalDetectorinMIMO-OFDMSystemsGA-Grover’sQuantumSearchAlgorithm4OutlineConclusions55321SimulationResults41Motivation42QuantumComputation&Grover’sQuantumSearch

Algorithm1QuantumComputationQuantumparallelismAnewmodeofcomputation,thatarebeyondthecapabilitiesofanyclassicalcomputationForexample,aclassicalcomputercanbeestimatedattaking1500yearstofactora232digitsnumber,whereasaquantumcomputerwouldtakearound20secondsGrover’sQuantumSearchAlgorithmAunsorteddatabasesearchalgorithmbasedonQCIfthesearchspacehasNentries,thenthetimetakentocompleteasearchisO(N).Noclassicalalgorithmcandobetterthanthis

Grover’salgorithmworksintimeForlargeN,thiscouldyieldverylargeperformanceincreasesForexample,tosearchanamefrom10,000entriesinasmallcitytelephonedirectory,classicalalgorithmcanbeestimatedattaking5,000stepswhereasGrover’salgorithmwouldtakeonly100steps!MIMO-OFDMsignaldetectioncanbeformulatedasaproblemtosearchtheoptimalsolutionThatisthemotivationforustoapplyGroverAlgorithmtosignaldetectioninMIMO-OFDMsystemsGrover’sQuantum

SearchAlgorithm43BasicconceptsofQCQuantumBit2PartAQuantumRegisterN=2nstatescanbestoredinthen-bitQregisteratthesametime

orqubitQuantumparallelism

orQregisteranylinearhermitianoperatorUoperatingonaqregisterisexecutedparallel

onallN=2nstoredstatesMechanismofGAPartB44readtheresultoff(x)=1

Initialization.PrepareaQregisterGroverIteration

SelectiveInversion

InversionaboutAverage

TerminationconditionMeasurementYesNoPerformtheselectivephaseinversionbyOracleoperatormisthenumberofthesolutionsGrover’sQuantum

SearchAlgorithm2

PartC45PerformanceEvaluationofGAFig.1TherelationshipbetweenPandi

Pistheprobabilityofsearchingthedesiredanswer,andiistheiterationtimesn----numberofqubitsN=2n----numberofdatabaseentriesI

----optimalnumberofiterationsP----probabilityofobtainingtheoptimalsolutiontheoptimalnumberofevaluationsis71Grover’sQuantum

SearchAlgorithm2

PartD46ImprovedGrover’sAlgorithmFig.2TherelationshipbetweenPandi

Pistheprobabilityofsearchingthedesiredanswer,andiistheiterationtimesMoreiterationswillreducetheprobabiltyofobtainoptimalsolutionTheprobabilityofobtainingtheoptimalsolutionNentries,msolutionsGrover’sQuantum

SearchAlgorithm2

PartD47ImprovedGrover’sAlgorithmTheprobabilityofobtainingtheoptimalsolutionNentries,msolutionsIncaseofm=N/2,θ=π/4,theprobabilityofobtainingtheoptimalsolutionis0.5andthefailurerateisalso0.5,nomatterhowmanyiterationsGrover’sQuantum

SearchAlgorithm2

PartD48ImprovedGrover’sAlgorithmWeconsideranImprovedGroveralgorithmasfollowsGrover’sQuantum

SearchAlgorithm2

PartD49ImprovedGrover’sAlgorithmWeconsideranImprovedGroveralgorithmasfollowsPGAIGAFig.3P~m/NIGA:Incaseofm=0.5N,P=1P≥98.01%,m>=0.25N,i=1Grover’sQuantum

SearchAlgorithm2GABasedSignalDetectorinMIMO-OFDMSystems50RemovecpFFTRemovecpFFTRemovecpFFTSignalDetectionSRx-1Rx-2Rx-M

...

...3ThediagramofMIMO-OFDMreceiverFig.4ThestructureofMIMO-OFDMsignaldetectorGABasedSignalDetectorinMIMO-OFDMSystems51MIMO-OFDMdetectionalgorithms1.OptimumDetection(Maximumlikelihood,ML)

theoptimalreceiverthebesthighcomplexity2.LinearDetection(Zero-Forcing,ZF;Minimum-Mean-Square-Error,MMSE)

lowcomplexity

limitedperformance3.Non-linearDetection(VerticalBellLayeredSpaceTime,VBLAST)

thebesttradeoffbetweenperformanceandcomplexity

difficulttoimplementforit’sintensivecomputation 3Thecomplexityofsearchingtheglobaloptimumbyexhaustivesearchis

GABasedSignalDetectorinMIMO-OFDMSystem52GABasedDetector3Fig.5ThestructureofGA-baseddetectorRemovecpFFTRemovecpFFTRemovecpFFTSRx-1Rx-2Rx-M......DatabaseConstructionGrover’sAlgorithmGABasedSignalDetectorinMIMO-OFDMSystem53DatabaseConstruction3nTqubitQregistersstoreall2nT

transmittedsequencesDatabase1SameIndexSearchtheindexofinDatabase2byGAstoreall

2nT

decisionvaluesDatabase2forallxieobtaintheoptimalsolutionSimulationResults544Fig.6.BitErrorRatiovs.Signal-NoiseRatio,BPSK,incorrectsolutionP=0.001Fig.7.BitErrorRatiovs.Signal-NoiseRatio,QPSK,incorrectsolutionP=0.001Itisevidentthattheproposed

GDdetectoroutperformstheMMSEandVBLAST-MMSEdetectorintheperformanceofBitErrorRate,closetotheoptimalMLdetectorSimulationResults554Fig.8.BitErrorRatiovs.Signal-NoiseRatio,QPSK,incorrectsolutionP=0.00001Fig.9.BitErrorRatiovs.Signal-NoiseRatio,QPSK,incorrectsolutionP=0.00001ItisevidentthattheproposedIGDdetectorisclosertotheoptimalMLdetectoreveninP=0.00001.TheprobabilityofGrover’salgorithmobtainingtheincorrectsolutionPis0.00001.Inthiscase,theperformanceofGDdetectordeclines

ThemostimportantisthatthecomplexityofGDandIGDisIt’smuchbetterthanclassicalMLdetectorwhichcomplexityisConclusion56ConclusionASPEN5Grover’squantumsearchAlgorithm(GA)canfindouttheglobaloptimaonlytakingstepsAnImprovedGA(IGA)isproposedNovelsignaldetectorsinMIMO-OFDMsystembasedonGAandIGAareproposedThesimulationresultsshowthattheproposedGAandIGA

baseddetectorsoutperformMMSEandVBLAST-MMSEbaseddetector,closetooptimalMLbaseddetectorandhavelowercomplexitythanML

ThankYouforyourattention!Q&AQuantum

Genetic

Algorithm《智能信息處理與量子計算》第3講2024/8/2259GeneticAlgorithmQuantumGeneticAlgorithmOutline212024/8/2260Geneticalgorithm

遺傳算法（GeneticAlgorithm,GA）是模擬達爾文生物進化論的自然選擇和遺傳學(xué)機理的生物進化過程的計算模型，是一種通過模擬自然進化過程搜索最優(yōu)解的方法。2024/8/2261Geneticalgorithm

2024/8/226262Geneticalgorithm

進化計算是一種成熟的具有高魯棒性和廣泛適用性的全局優(yōu)化方法，具有自組織、自適應(yīng)、自學(xué)習(xí)的特性，能夠不受問題性質(zhì)的限制，有效地處理傳統(tǒng)優(yōu)化算法難以解決的復(fù)雜問題。2024/8/22632024/8/22642024/8/22652024/8/2266復(fù)制2024/8/22672024/8/22682024/8/2269父代子代2024/8/2270父代子代2024/8/2271基本遺傳算法1.隨機產(chǎn)生一個由固定長度字符串組成的初始群體(種群);2.對于字符串種群，進行下述迭代，直到選種標(biāo)準(zhǔn)被滿足為止：計算群體中的每個個體字符串的適應(yīng)度值(fitness);進行以下三種操作(至少前兩種)來產(chǎn)生新的群體:選擇:把現(xiàn)有的個體字符串復(fù)制到新的群體中。雜交:通過遺傳重組隨機選擇兩個現(xiàn)有的子字符串,產(chǎn)生新的字符串。變異:將現(xiàn)有字符串中某一位的字符隨機變異。將后代中具有最高適應(yīng)值的個體字符串指定為遺傳算法運行的結(jié)果。這一結(jié)果可以是問題的解(或近似解)。2024/8/2272遺傳算法一般步驟2024/8/22732024/8/22742024/8/2275GeneticAlgorithmQuantumGeneticAlgorithmOutline212024/8/2276MechanismofGAQuantumGeneticAlgorithmQuantumGeneticAlgorithm(QGA)proposedcantreatthebalancebetweenexplorationandexploitationmoreeasilywhencomparedwithconventionalgeneticalgorithm(GA)QGAcanexplorethesearchspacewithasmallernumberofindividualsandexploitthesearchspaceforaglobalsolutionwithinashortspanoftime

2024/8/2277QuantumGeneticAlgorithmQuantumBitRepresentationor

qubitwhereα

andβarecomplexNumbers|α|2+|β|2=1AQ-bitmaybeinthe“1”state,inthe“0”state,orinanylinearsuperpositionofthetwo

states

(1)2024/8/2278QuantumGeneticAlgorithmQuantumBitQuantumGeneapairofnumbers(α,β)as[α

β]T,(α,β)correspondsaqubitor

qubitQuantumChromosomeastringofkQ-genesorQ-geneor

Q-ChromosomeRepresentation(2)2024/8/2279MechanismofGAQuantumGeneticAlgorithmAthree-Q-bitChromosomewiththreepairsofamplitudessuchas

(3)2024/8/2280MechanismofGAQuantumGeneticAlgorithmThenthestatesofthethree-Q-bitChromosomecanberepresentedasTheaboveresultmeansthattheprobabilitiestorepresentthestates

|000>,|001>,|010>,|011>,|100>,|101>,|110>,|111>are

3/32,9/32,1/32,3/32,3/32,9/32,1/32,3/32(4)2024/8/2281MechanismofGAQuantumGeneticAlgorithmApopulationofQuantumindividuals（Chromosome）isdefinedas(5)wherenisthesizeofpopulation,andqjtisaQuantumindividual2024/8/2282MechanismofGAQuantumGeneticAlgorithmAQ-gate

isdefinedasavariationoperatorofQGA(6)Theadjustmentoperationisasfollows(7)2024/8/2283MechanismofQGAQ(t)isapopulationofQ-chromosomesisaQ-chromosome

U(θ)isaQuantumrotationgateBeginInitializationQ(t)MakeP(t)bymeasureQ(t)EvaluatefitnessRecordthebestTerminationconditionUpdatebyQ-gatesEndYesNo2024/8/2284ThankYouforyourattention!Q&A2024/8/2285MechanismofGAQuantumGeneticAlgorithmTheprocedureofQGA2024/8/2286MechanismofGAQuantumGeneticAlgorithmOverallstructureofQGAkqubitCollapseBasestateBinarystringf(x)>f(b)?QGAanditsApplication《智能信息處理與量子計算》第4講2024/8/2288QGAPerformanceOutline21QGAforMIMO-OFDMDetection3QGAforCognitiveRadioSpectrumSharing2024/8/2289QGAPerformance

RepresentationQuantumBitPartAQuantumGeneapairofnumbers(α,β)as[α

β]T,(α,β)correspondsaqubitor

qubitQuantumChromosomeastringofkQ-genesorQ-geneor

Q-Chromosome2024/8/2290QGAPerformance

MechanismofQGAQ(t)isapopulationofQ-chromosomesisaQ-chromosome

U(θ)isaQuantumrotationgatePartBBeginInitializationQ(t)MakeP(t)bymeasureQ(t)EvaluatefitnessRecordthebestTerminationconditionUpdatebyQ-gatesEndYesNo2024/8/2291MechanismofGAQuantumGeneticAlgorithmTheprocedureofQGA2024/8/2292MechanismofGAQuantumGeneticAlgorithmOverallstructureofQGAkqubitCollapseBasestateBinarystringf(x)>f(b)?2024/8/2293QGAPerformance

PartCPerformanceEvaluationforQGAAnon-convexfunctionusedasaperformancetestproblemforoptimizationalgorithmsintroducedbyHowardH.Rosenbrockin1960AlsoknownasRosenbrock'svalleyorRosenbrock'sbananafunctionTheglobalminimumisinsidealong,narrow,parabolicshapedflatvalley.Tofindthevalleyistrivial.Toconvergetotheglobalminimum,however,isdifficultFig.1Rosenbrockfunction2024/8/2294QGAPerformance

PartCPerformanceEvaluationforQGAaglobaloptimizationtestfunctionwithseverallocalminimaFig.2Goldstein-Pricefunction2024/8/2295QGAPerformance

PartCPerformanceEvaluationforQGAFig.3ConvergenceprocessofGAandQGAforRosenbrockfunctionFig.4ConvergenceprocessofGAandQGAforGoldstein-PricefunctionQGAcanconvergetowardtheoptimalsolutionmorequicklythanGA2024/8/2296QGAPerformanceOutline21QGAforMIMO-OFDMDetection3QGAforCognitiveRadioSpectrumSharing2024/8/2297QGAforMIMO-OFDMDetectionMIMOAdvantagesDisadvantagesHighspectralefficienciesSevereinter-symbolinterference(ISI)OFDMAdvantagesDisadvantagesRobusttofrequencyselectivefadingchannelsLowspectralefficienciesMIMO-OFDMMIMO-OFDMSystem2024/8/2298QGAforMIMO-OFDMDetectionRemovecpFFTRemovecpFFTRemovecpFFTSignalDetectionSRx-1Rx-2Rx-M

...

...ThediagramofMIMO-OFDMreceiver2024/8/2299QGAforMIMO-OFDMDetectionMIMO-OFDMdetectionalgorithms1.OptimumDetection(Maximumlikelihood,ML)

theoptimalreceiverthebesthighcomplexity2.LinearDetection(Zero-Forcing,ZF;Minimum-Mean-Square-Error,MMSE)

lowcomplexity limitedperformance3.Non-linearDetection(VerticalBellLayeredSpaceTime,VBLAST) thebesttradeoffbetweenperformanceandcomplexity difficulttoimplementforit’sintensivecomputation 2024/8/22100QGAforMIMO-OFDMDetectionTheBlockDiagramofQGABasesDetectorRemovecpFFTQGADETECTIONRemovecpFFTRemovecpFFTSRx-1Rx-2Rx-M

...

...2024/8/22101QGAforMIMO-OFDMDetectionMainparameters1.Thegenenumberofqubitinquantumchromosomeisequaltothenumberofantennas

M.2.Thefitnessfunctionisbasedonmaximumlikelihoodrule:3.TerminateconditioniswhenthenumberofiterationsisequaltoG(generationnumber)2024/8/22102QGAforMIMO-OFDMDetectionSimulationresultsFig.7BitErrorRatiovs.Signal-NoiseRatio,BPSKFig.8BitErrorRatiovs.Signal-NoiseRatio,QPSK2024/8/22103QGAforMIMO-OFDMDetectionConclusionsComparedtothewell-knowVerticalBellLayeredSpaceTime(VBLAST)algorithm,thecomplexityoftheproposedschemeisreducedThesimulationresultsshowthattheQGAbaseddetectorismuchbetterthanVBLASTdetector,namelya2dBgaininperformancecanbeachievedBesidestheproposeddetectorisobviouslysuperiortotheGAbaseddetector2024/8/22104QGAPerformanceOutline21QGAforMIMO-OFDMDetection3QGAforCognitiveRadioSpectrumSharing2024/8/22105QGAforCognitiveRadioSpectrumSharingLimitedandinefficientspectrumresources2024/8/22106QGAforCognitiveRadioSpectrumSharingSpectrumallocationmodelbasedongraphtheoryAuctionbiddingmodelInterferencetemperaturemodelGametheorymodel

-Cooperativegametheorymodel-Non-cooperativegametheorymodelFourmainspectrumallocationmodels2024/8/22107QGAforCognitiveRadioSpectrumSharingNon-cooperativegamemodelweselectthecapacityavailabletotheCRuser(theplayer)astheutilityfunction2024/8/22108QGAforCognitiveRadioSpectrumSharingNon-cooperativegamemodelInnon-cooperativegames,eachCRuserwilltrytogetmorefrequencybandsforitsownandmaximizeitsownutilityfunction.Thisprocesscanbeexpressedas2024/8/22109QGAforCognitiveRadioSpectrumSharingNon-cooperativegamemodelweusesumcapacityofallCRusersastheutilityfunction,thusthegamewillbetakentothesocialoptimalpoint(themaximalsumcapacitypoint)Thespectrumsharingproblemcanbedefinedasthefollowingoptimizationproblem:2024/8/22110QGAforCognitiveRadioSpectrumSharingCRusers’powerPiBasestateQGA-SS2024/8/22111QGAforCognitiveRadioSpectrumSharingincreasethepopulation’sdiversity2024/8/22112QGAforCognitiveRadioSpectrumSharingFig.9SumcapacityversuspopulationsizeFig.10SumCapacityconvergencewithgenerationsSimulationResults2usersCRNetwork2024/8/22113QGAforCognitiveRadioSpectrumSharingFig.11SumcapacityversusgenerationsPopulationSize60,3ChannelsFig.12SumcapacityversusgenerationsPopulationSize60,4ChannelsSimulationResults4usersCRNetwork2024/8/22114QGAforCognitiveRadioSpectrumSharingAnovelcognitiveradiospectrumsharingschemebasedonQGAisproposedTheproposedschemeshowsbetterconvergencerateandhighersumcapacitythanGAbasedscheme

-notonlyintwo-userCRNetworkbutalsoinmulti-userCRNetworkThecapacityisaffectedbypopulationsizeofQGA

-developapopulationadaptationschemeforQGAbasedCRinthefutureworkConclusions2024/8/22115QGAPerformanceQGAforMulti-userDetectionOutline21QGAforMIMO-OFDMDetection3QGAforCognitiveRadioSpectrumSharing42024/8/22116QGAforMulti-userDetectionThestructureofQGAbasedMUD2024/8/22117QGAforMulti-userDetectionThereceivedsignalr(t)iswhereEk

,theenergyofthekthuserαk

,thepathgainofthekthuser

τk,thedelayofthekthuser

bk

,thesymbolofthekthuser

sk(t),thecontinuoussignaturesignaln(t),zeromeanwhiteGaussiannoise2024/8/22118QGAforMulti-userDetectionTheykistheoutputofthematchedfilterwhere2024/8/22119QGAforMulti-userDetectionSearchfortheglobaloptimumof(1),wecanobtainthedesiredresults(1)ProvedtoberathertiresomeWeuseQGAtosearchtheoptimum2024/8/22120QGAforMulti-userDetectionTheQGA-MUDAlgorithm

Theobjectivefunctionis(2)Thefitnessfunction(3)whereμis0.05insimulation2024/8/22121QGAforMulti-userDetectionTheresultsshowthatthedetectionperformanceoftheproposeddetectorisgettingbetterandbetterwiththeincreaseofpopulationsize(P)andgenerationnumber(G)Fig.5BitErrorRatiovs.Signal-NoiseRatioofQGA-MUD2024/8/22122QGAforMulti-userDetection

theproposedQGA-MUDoutperformstheGA-MUDinbit-errorrate

Fig.6BitErrorRatiovs.Signal-NoiseRatio2024/8/22123QGAforMulti-userDetectionAnovelmulti-userdetectionschemebasedonQuantumGeneticAlgorithmisproposedQGA-MUDresultedinbetterperformancethanGA-MUD,namelya2-3dBgaininperformancecanbeachievedTheresultsdemonstratedtheeffectivenessandtheapplicabilityofQGAinmulti-userdetectionConclusions2024/8/22124ThankYouforyourattention!Q&AQuantum

NeuralNetworks《智能信息處理與量子計算》第5講量子智能計算126ArtificialNeuralNetworkQuantumNeuralNetworkOutline21量子智能計算127ArtificialNeuralNetwork量子智能計算128ArtificialNeuralNetwork量子智能計算129ArtificialNeuralNetwork量子智能計算130ArtificialNeuralNetwork人工神經(jīng)元量子智能計算131ArtificialNeuralNetwork人工神經(jīng)元（Neuron）各突觸的權(quán)值偏置,即閥值量子智能計算132ArtificialNeuralNetwork激活函數(shù)(Activationfunctions)sigmoidfunction量子智能計算133ArtificialNeuralNetwork組成人工神經(jīng)網(wǎng)絡(luò)的三要素：神經(jīng)元，網(wǎng)絡(luò)拓撲，學(xué)習(xí)算法網(wǎng)絡(luò)模型

靜態(tài)神經(jīng)網(wǎng)絡(luò)動態(tài)神經(jīng)網(wǎng)絡(luò)多層感知器模型（MLP）徑向基函數(shù)網(wǎng)絡(luò)（RBF）自組織特征映射網(wǎng)絡(luò)（SOFM）時延神經(jīng)網(wǎng)絡(luò)遞歸神經(jīng)網(wǎng)絡(luò)量子智能計算134ArtificialNeuralNetwork

－多層感知器是信號處理中應(yīng)用最多的神經(jīng)網(wǎng)絡(luò)結(jié)構(gòu)

－多層感知器是一種前饋神經(jīng)網(wǎng)絡(luò)，由輸入層、輸出層和若干中間層(常稱為隱層，hidden-layer)組成

-多層感知器(MLP,MultilayerPerceptron)量子智能計算135ArtificialNeuralNetwork量子智能計算136ArtificialNeuralNetwork量子智能計算137ArtificialNeuralNetwork-徑向基函數(shù)網(wǎng)絡(luò)(RBF,RadialBasisFunctions)量子智能計算138ArtificialNeuralNetwork-自組織特征映射網(wǎng)絡(luò)

(SOFM:Self-organizationFeatureMap)右圖為用作離散映射的二維神經(jīng)元格型結(jié)構(gòu)的SOFM網(wǎng)絡(luò)，其中每個神經(jīng)元全連接到輸入層的所有源節(jié)點；它是一個行-列排列的神經(jīng)元組成的單層前饋網(wǎng)絡(luò)主要用于實現(xiàn)對輸入特征向量的聚類量子智能計算139ArtificialNeuralNetwork-時延神經(jīng)網(wǎng)絡(luò)(TDNN)MLPLTDx(n)y(n)x(n)x(n-1)…x(n-p)MLPLTD1x(n)x(n)x(n-1)…x(n-p)LTD2y(n-q)y(n-2)y(n-1)Z-1對應(yīng)于非線性IIR(即非線性ARMA)對應(yīng)于非線性FIR(即非線性MA)量子智能計算140ArtificialNeuralNetwork-遞歸神經(jīng)網(wǎng)絡(luò)(RecurrentNeuralNetworks)Hopfield神經(jīng)網(wǎng)絡(luò)全連接的反饋網(wǎng)絡(luò)

Hopfield神經(jīng)網(wǎng)絡(luò)是基于內(nèi)容尋址的記憶系統(tǒng)實現(xiàn)聯(lián)想記憶存儲系統(tǒng)能保證收斂到局部極小值二進制閾值單元Z-1Z-1Z-1Z-1單元延時xiyi量子智能計算141ArtificialNeuralNetwork訓(xùn)練（training），又稱學(xué)習(xí)（learning）-神經(jīng)網(wǎng)絡(luò)訓(xùn)練

量子智能計算142ArtificialNeuralNetwork-訓(xùn)練規(guī)則

Hebb學(xué)習(xí)規(guī)則(相關(guān)學(xué)習(xí))(無師學(xué)習(xí))

其中

WTA(Winner-Take-All)(競爭)學(xué)習(xí)規(guī)則(無師學(xué)習(xí))

其中

δ學(xué)習(xí)規(guī)則(誤差修正學(xué)習(xí))(有師學(xué)習(xí))其中ε為代價函數(shù)。

量子智能計算143ArtificialNeuralNetwork-訓(xùn)練算法與神經(jīng)網(wǎng)絡(luò)模型相關(guān)如：多層感知器模型——BP學(xué)習(xí)算法量子智能計算144ArtificialNeuralNetwork《量子智能計算》145ArtificialNeuralNetworkQuantumNeuralNetworkOutline21量子智能計算146Motivation人工神經(jīng)網(wǎng)絡(luò)（ANN）的優(yōu)勢

并行分布式處理、魯棒性人工神經(jīng)網(wǎng)絡(luò)（ANN）的缺陷

耗時的訓(xùn)練、有限的記憶容量量子神經(jīng)網(wǎng)絡(luò)（QNN）具有以下一些優(yōu)點，可以克服ANN的某些缺陷量子智能計算147exponentialmemorycapacityhigherperformanceforlowernumberofhiddenneuronsfasterlearningeliminationofcatastrophicforgettingduetotheabsenceofpatterninterferencesinglelayernetworksolutionoflinearlyinseparableproblemsprocessingspeed(1010bits/s)smallscale(1011neurons/mm)higherstability