0310量子机器学习

QuantummachinelearningDeeplearninganditsapplicationsQuantumMachineLearningQMLisanovelsubjectcombinedboththestrengthofquantumcomputing(QC)anduniversalityofmachinelearning(ML).Fourdifferenttypesofresearch:WhatisQML?BenefitofQMLExtractsomeatypicalpatternsHavlíčekV,CórcolesAD,TemmeK,etal.Nature,2019.LiuY,ArunachalamS,TemmeK.NaturePhysics,2021.LearningefficiencyimprovementZhaoZ,FitzsimonsJK,etal.Phys.Rev.A,2019.KerenidisI,LandmanJ.Phys.Rev.A,2021.BusinessesandOrganizationsQuantumexperimentsHuangHL,DuY,etal.Phys.Rev.Appl.,2021.RobertA,BarkoutsosPK,etal.npjQuantumInf.,2021.ImagegenerationProteinfoldingTypicaldevelopmentofQMLCategoryMethodQuantumBasicLinearAlgebraSubroutines-basedQuantumprincipalcomponentanalysisLloyd,S.,Mohseni,M.&Rebentrost,P.Nat.Phys,2014.QuantumsupportvectormachineRebentrost,P.,Mohseni,M.&Lloyd,S.Phys.Rev.Lett.,2014.QuantumclusteringLloydS,MohseniM,Rebentrost.arXiv:1307.0411,2013.Quantumk-meansKerenidisI,LandmanJ,LuongoA,etal.

NeurIPS,2019.Quantumkernel-basedQuantum-enhancedfeaturespacelearningHavlíčekV,CórcolesAD,TemmeK,etal.Nature,

2019.ProjectedquantumkernelHuang,HY.,Broughton,M.,Mohseni,M.etal.Nat.

Comm.,2021.QuantumDeepLearningQuantumrecurrentneuralnetworkBauschJ.

NeurIPS,2020.QuantumdeepneuralnetworkBeerK,BondarenkoD,FarrellyT,etal.Nat.

Comm.,2020.Quantumcomputing4SJTUDeepLearningLecture.QuantumComputingharnessesthelawsofquantummechanicstosolveproblemstoocomplexforclassicalcomputers.QuantumSuperpositionQuantumEntanglementQuantumDevicesFastprogressofquantumdevicesDifferenttechnologiesSuperconducting,Trappedion,Neutralatom,Photonics,etc.5SJTUDeepLearningLecture.IBM

127QubitGoogle

53QubitsIonQ

32+Qubits6SJTUDeepLearningLecture.QuantumComputerRoadmapQuantumComputerRoadmapThenumberofqubitsincreasesexponentiallyovertimeThecomputingpowerincreasesexponentiallywiththenumberofqubits7SJTUDeepLearningLecture.IBMQuantumQuantumComputinginNISQEra8SJTUDeepLearningLecture.IBMQuantumNoisyIntermediate-ScaleQuantum(NISQ)Limitednumberofqubits:tenstohundredsofqubitsNoisy:qubitsaresensitivetoenvironment;quantumgatesareunreliableLimitedconnectivity:noall-to-allconnections/IBMQGateErrorRateGoogleSycamore53QIBMWashington127Q//articles/s41586-019-1666-59SJTUDeepLearningLecture.UniversalQuantumComputation（NISQ）where

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learning10SJTUDeepLearningLecture.QuantumAlgorithms’Progression1992~1994指数级加速的量子算法(Deutsch-Jozsa,Shor因子分解，离散对数算法)2007HHL算法

解线性方程

2008量子支持向量机、量子主成分分析2013变分量子线路（VQE）2016量子近似优化算法（QAOA）2019量子卷积神经网络（QCNN）…requirebig,perfectquantumcomputers.Hybridquantum/classicalalgorithms,noise-robust.QuantumMachineLearningQuantumLinearAlgebraFault-tolerantvsNear-termVariationalquantumAlgorithm2019QuantumConvolutionNeuralNetwork(QCNN)

Quantumcomputing11SJTUDeepLearningLecture.QuantumSuperpositionQuantumEntanglementJohnvonNeumann.MathematicalFoundationsofQuantumMechanics(1932)

QuantumBit12SJTUDeepLearningLecture.QuantumBit(Qubit)

Anarbitraryquantumstates:QuantumBit13SJTUDeepLearningLecture.

QuantumGates14SJTUDeepLearningLecture.Qubitgates:operationsononequbitormultiplequbitsThequbitgatescanberepresentedwithmatrixformatwithdimensionAllgatematricesareunitarymatrices:theconjugatetransposeisthesameasitsinverseSinglequbitgates:

Pauligate(xyz):QuantumCircuit15SJTUDeepLearningLecture.Measurement:ameasurementcollapsesaqubit'sstatetooneofitsbasisstates:|0⟩or|1⟩

QBLAS-basedQML

16SJTUDeepLearningLecture.BiamonteJ,WittekP,PancottiN,etal.Quantummachinelearning[J].Nature,2017.QBLAS-basedQML

17SJTUDeepLearningLecture.inputqubitsunitaryoperationsmeasurementsmultiplytraceQBLAS-basedQML

18SJTUDeepLearningLecture.Theintuitionbehindquantumspeedups

ClassicalbitsQuantumbits(qubits)QBLAS-basedQML19SJTUDeepLearningLecture.QuantumparallelismInquantumcomputers,theresultsforallpossibleinputdataarecomputedinparallel.SequentialcomputationInputdata001010101101010100001010101101010100OutputdataClassicaldataprocessingQuantumdataprocessingQBLAS-basedQMLEncodeinputdata(vectors/matrices)asquantumstates;UseQBLAStocomputeanalgebraicexpressionoftheinput;Theadvantageofquantumalgorithms,isthathigh-dimensionalvectorscanberepresentedusingonlyafewqubits,suchthatweonlyneedtodealwiththeproblemthathasthelogarithmicsizeoftheoriginaldata.Extractinformationfromtheoutput(i.e.anestimatorofadesiredvalue)20SJTUDeepLearningLecture.AtypicalapplicationofQBLAStomachinelearningInputdataMorelinearalgebraclassicalalgorithmquantumalgorithm①②③somelinearalgebra21SJTUDeepLearningLecture.QBLAS-basedQMLLandscape:quantumspeedupsinquantummachinelearningTaskPublicationTaskPublicationPrincipalcomponentanalysisNat.Phys.2014SparselinearprogrammingPRL2009Semidefiniteprogramming2016DatafittingPRL2012Low-rankmatrixdecompositionPRA2018TopologydataanalysisNat.Comm.2016SupportvectormachinePRL2014GaussianprocessregressionPRA2019K-meansNIPS2019SupervisedclusteringPRL2001BayesianinferencePRA2014Recommendationsystems2016VariationalQuantumMachineLearningN-bodyProblemsCombinatorialOptimizationProblemsImageClassificationTasks…SJTUDeepLearningLecture.HybridLearningParadigmSJTUDeepLearningLecture.ClassicalSystemStatePreparationCalculatinglossCalculatingGradientOptimize/UpdateParametersQuantumSystemExecutethePQCMeasuretheoutputstateParameterizedQuantumCircuitSingle-qubitParameterize