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11 APRIL 2018MUNICH, GERMANY

KristenPudenzSeniorQuantumApplicationsEngineer

LOCKHEED MARTIN SITE UPDATE

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THE USC-LM QUANTUM COMPUTING CENTER

Dr.EdwardH.“Ned”AllenChiefScientistandLMSeniorFellowLockheedMartinCorporation

UniversityofSouthernCaliforniaInformationSciencesInstituteMarinadeRey,California,USA

GregTallantProgramManagerandLMFellow

LockheedMartinAeronauticsSkunkWorks

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QUANTUM APPLICATIONS TEAM

KristenPudenz,Ph.D.QuantumApplicationsQuantumErrorCorrection

SteveAdachi,Ph.D.QuantumMachineLearningLMFellow,SpaceSystems

JuliaKwok,M.E.E.QuantumGraphColoringClassicalOptimization

ChrisElliott,Ph.D.QuantumEnabledV&V15+YearsofFlightControlDevelopment

PeterStanfill30+YearsofFlightControl

Development

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CENTER HISTORY AND TIMELINE• Early2010- LMidentifiedquantuminformationscienceasa

highpotentialtechnologytoaddresscriticalneeds

• Nov2010- PurchasedaccesstimeandsupportforDW-1Rainierquantumannealer fromD-WaveSystems

• Mar2011- FormedpartnershipwithUSC/ISItohostDW-1andestablishcollaborativeQCCenter

• Jan2012- USC-LMQCCenterOperational

• Mar2013– Completedupgradeto512-qubitDW-2Vesuviusprocessor

• Feb2016– Completedupgradeto1000+-qubitDW-2XWashingtonprocessor

MarinadelRey,CA

photo creditFatemeh Kashfi.

DW-1Rainier

DW-2Vesuvius

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MACHINE LEARNING: CONNECTION PRUNING EXPERIMENT• Question:HowmuchqubitconnectivityisneededforMachineLearning?

• RestrictedBoltzmannMachine(RBM)caninprinciplebeafullbipartitegraph

• WeknowwecanachievegoodMachineLearningperformanceusingfullbipartiteRBMs

• D-Wave“Chimera”graphcorrespondstoaLocallyConnectedBoltzmannMachine(LCBM)

• EvidencesuggestssuchLCBMsaretoosparseforgoodMLperformance

• IstheresomeintermediaterangeofsparsitythatisrealizableonQAhardware,yetstillgives

goodMLperformance?

• CharacterizingMachineLearningapplicationneedsforqubitconnectivitymayhelptoinformQEOarchitecturedesign

• Startwithanalready-trained,fullbipartiteRBM

• Defineacutoff! andpruneconnectionswith "#$ < !• MeasureaccuracyoftheprunedRBMonthetraining/testset

• KeepincreasingCandobservehowaccuracydeteriorates

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EXAMPLE DEEP BELIEF NET• Coarse-grained”MNIST(CG-MNIST)

• Eachtraining/testimageconsistsof32superpixels

• Modeledusing(32,32,32,10)DeepBeliefNet

• Inputlayerwith32nodes

• 2hiddenlayerswith32nodeseach

• Outputlayerwith10nodes

• RBMlayers

• Layer1=32x32RBM

• Layer2=32x32RBM

• Layer3=32x10RBM

originalimage

coarse-grainedimage

Adachi, S.H., Henderson, M.P. (2015) Application of Quantum Annealing to Training of Deep Neural Networks. http://arxiv.org/abs/1510.06356

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EFFECT OF PRUNING CONNECTIONS ON ACCURACY

Inthisexample,wecanpruneoverhalfthelayer1and2connectionswithminimaldecreaseinaccuracy

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WHAT DO THE PRUNED NETWORKS LOOK LIKE?

PrunedOriginal

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CONNECTIVITY EFFECTS

Mostnodeshavedegreelessthanorequalto16

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MOVING FORWARD• Pruningafterthefactischeating

• Doesn’ttellusbeforewetrain,whichconnectionswecandowithout

• SuggestshoweverthatwecanachievegoodMLperformancewithoutfullbipartiteconnectivity• Nextstepistotryquantum-assistedtrainingofnetworksthathavesparserconnectivityfromthestart

• CouldseeaslighttradeoffsincesparserRBMscanbeembeddedonChimerausingshorter-lengthchains• WhatkindofneuralnetworkcouldbeembeddedonPegasusarchitecture?

• Weneedtobecarefulaboutthewayinwhichquantumannealers approximatetheBoltzmanndistribution• Temperatureestimation• Othermethodsofmeasuringandcontrollingdistancebetweengatheredsamplesandidealdistribution

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GRAPH COLORING• Wearepursuingagreedyapproachbasedonfindingonecolor’svertexsetatatimeonthequantum

annealer usingmaximumindependentset(MIS)orvertexcover(VC)• Thisallowsustocolorgraphsbyembeddingannvariableproblem

• Globalgraphcoloringapproachrequiresn*kvariables

• ClassicalcomputingclosestheloopformultipleMISorVCcyclestofindeachcolorsuccessively

• Findoneindependentset– thisisonecolor

• Removeindependentsetfromgraph

• Findnextindependentsetandcontinuetheloopuntilallverticesarecolored

• WeareexaminingthefullalgorithmonatestsetofparameterizedErdos-Renyi graphstofacilitatecomparisonstopreviousresultsusingtheglobalapproach

• Embeddingthegraphtobecoloredtakesmostoftheclassicalcomputetime

• Weareinvestigatingmethodsofadjustingthefirstembeddingtomakeacompactyeteasytocomputeembeddingforsubsequentsubgraphsasindependentsetsareremoved

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COLORING RESULTS• Formanygraphs,wefind

ak-coloringthatissmallerthantheoneplantedatinstancegeneration

• Wedoseesomek-coloringswithlargerthanplantedk

• Wearecurrentlyworkingonanimprovedalgorithmthatshouldhavebetterresultswithslightlymoreclassicalcomputetime

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