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Alejandro Perdomo-Ortiz Senior Research Scientist, Quantum AI Lab. at NASA Ames Research Center and at the University Space Research Association, USA Honorary Senior Research Associate, Computer Science Dept., UCL, UK National Harbor, MD, September 28, 2017 Opportunities and challenges in quantum-enhanced machine learning in near-term quantum computers QUBITS D-wave User Group 2017 Funding: Perdomo-Ortiz, Benedetti, Realpe-Gomez, and Biswas. arXiv:1708.09757 (2017). To appear in the Quantum Science and Technology (QST) invited special issue on “What would you do with a 1000 qubit device?”
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Page 1: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

AlejandroPerdomo-OrtizSeniorResearchScientist,QuantumAILab.atNASAAmes ResearchCenterandatthe

UniversitySpaceResearchAssociation,USAHonorarySeniorResearchAssociate,ComputerScienceDept.,UCL,UK

NationalHarbor,MD,September28,2017

Opportunitiesandchallengesinquantum-enhancedmachinelearninginnear-termquantumcomputers

QUBITSD-waveUserGroup2017

Funding:

Perdomo-Ortiz,Benedetti,Realpe-Gomez,andBiswas.arXiv:1708.09757 (2017).ToappearintheQuantumScienceandTechnology(QST)invitedspecialissueon“Whatwouldyoudowitha1000qubit device?”

Page 2: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

D-WaveSystemCapability1) As a discrete optimization solver:

2) As a physical device to sample from Boltzmann distribution:

Potential NASA applications: - planning- scheduling - fault diagnosis - graph analysis - communication networks, etc.

QUBO: Quadratic Unconstrained Binary Optimization (Ising model in physics jargon).

Computationally bottleneck

Our work: Benedetti et al. PRA 94, 022308 (2016)

• Algorithm uses the same samples that will be used for the estimation of the gradient

• We provide a robust algorithm to estimate the effective temperature of problem instances in quantum annealers.

NP-hard problem

⇠(s1, ..., sN ) =NX

j=1

hjsj +NX

i,j2E

Jijsisj

Given {hj, Jij}, find {sk = ± 1}that minimizes

P

Boltzman

/ exp[�⇠(s1, ..., sN )/Teff

]

Early work:Bian et al. 2010. The Ising model: teaching an old problem new tricks.

Follow-up work:Raymond et al. Global warming: Temperature estimation in annealers. Frontiers in ICT, 3, 23 (2016).

Widely used in unsupervised learning

Visible units

Hidden unitsRBM

Potential NASA applications: - machine leaning (e.g., training

of deep-learning networks)

Page 3: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Learning algorithm

MODELP ( Image )

DATASET

Unsupervised learning (generative models)

NO LABELS

Learn the “best” model distribution that can generate the same kind of data

Page 4: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Learning algorithm

MODELP ( Image )

LEARNED MODELP ( Image )

DATASET

Example application:Image reconstruction

Damaged image

Unsupervised learning (generative models)

NO LABELS

Learn the “best” model distribution that can generate the same kind of data

Reconstructed image

Page 5: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Learning algorithm

MODELP ( Label | Image )

LEARNED MODELP ( Label | Image )

Supervised learning (discriminative models)

Learn the “best” model that can perform a specific task

Example application:Image recognition

Predicted label

Image to be recognized

61

26624 98 66 175

Labels

DATASET

Page 6: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Anear-termapproachforquantum-enhancedmachinelearningState-of-the-artQML

- NeedforqRAM (caseofmostgate-basedproposal).

- Qubitsrepresentvisibleunits;issueforcaseoflargedatasets

- Mostpreviousproposedworkhavehighlyoptimizedpowerfulclassicalcounterparts(e.g.,ondiscriminative/classificationtasks)

Probabilistic programming

Potential impact across social and natural sciences, engineering, and more

Hypothesis: intractable sampling problems enhanced by quantum sampling

Deeplearning Others...Bayesian

inference

Lesson1:MovetointractableproblemsofinteresttoMLexperts(e.g.,generativemodelsinunsupervisedlearning).

Page 7: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Anear-termapproachforquantum-enhancedmachinelearning

Lesson2:Needfornovelhybridapproaches.

LEARNING

Stochastic gradient descent

Θt+1 = Θt + G [ P(s|Θt) ]

PREDICTIONS

F [ P(s|Θt) ]

HARD TO COMPUTE

Estimation assisted by sampling from quantum computer

DATA

s = {s1,…, sD}

Computationally bottleneck

Widely used in unsupervised learning

Visible units, v

Hidden units, uRBM

Ex.:RestrictedBoltzmannMachines(RBM)

hviujip(v,u)Where,p(v,u) =

e�E(v,u|✓)/Teff

Z(✓)

Perdomo-Ortiz,etal.OpportunitiesandChallenges inQuantum-AssistedMachineLearninginNear-termQuantumComputer.arXiv:1708.09757.(2017).

Benedetti,etal.Quantum-assistedlearningofgraphicalmodelswitharbitrarypairwiseconnectivity.arXiv:1609.02542 (2016).

Benedetti,etal.Estimationofeffectivetemperaturesinquantumannealers forsamplingapplications:Acasestudywithpossibleapplicationsindeeplearning.PRA 94,022308(2016).

Benedetti,etal.Quantum-assistedHelmholtzmachines:Aquantum-classicaldeeplearningframeworkfor industrialdatasetsinnear-termdevices.arXiv:1708.09784 (2017).

Challengessolved:

Page 8: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

X

v2D

@ lnL(✓|v)@Jij

/ hviujidata � hviujimodel

Anear-termapproachforquantum-enhancedmachinelearning

Challengesofthehybridapproach:

- Needtosolveclassical-quantummodelmismatch

Training Method: Stochastic gradient ascent

Benedettietal.Phys.Rev.A94,022308(2016)

Classical Quantum-Teff?

Nosignificantprogressin2010-2015forgenerativemodelingandQAsampling.

Visibleunits Hiddenunits

Page 9: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Anear-termapproachforquantum-enhancedmachinelearning

Resolvingmodelmismatchallowsforrestartingfromclassicalpreprocessing

Benedettietal.Phys.Rev.A94,022308(2016)

0 200 400 600 800 1000�11

�10

�9

�8

�7

�6

L av

(a)

With Bias CorrectionWithout Bias Correction

0 200 400 600 800 1000�11

�10

�9

�8

�7

�6

L av

(b)

With Importance SamplingWithout Importance Sampling

0 100 200 300 400 500iteration

�11

�10

�9

�8

�7

�6

L av

(c)QuALe @ TDW2X = 0.033 with RestartQuALe @ Te↵ with RestartCD-1

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Anear-termapproachforquantum-enhancedmachinelearning

Challengesofthehybridapproach:

Benedettietal.arXiv:1609.02542

Fullyvisiblemodels

Visibleunits

- Robustnesstonoise,intrinsiccontrolerrors,andtodeviationsfromsamplingmodel(e.g.,Boltzmann)

- Curseoflimitedconnectivity – parametersetting

- Needtosolveclassical-quantummodelmismatch

Training Method: Stochastic gradient ascent

Benedettietal.Phys.Rev.A94,022308(2016)

Classical Quantum-Teff?

X

v2D

@ lnL(✓|v)@Jij

/ hviujidata � hviujimodel

Visibleunits Hiddenunits

Nosignificantprogressin2010-2015forgenerativemodelingandQAsampling.

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Quantum-assistedunsupervisedlearningondigits

OptDigits Datasets

Dataset:OpticalRecognitionofHandwrittenDigits(OptDigits)

8x8 7x6 7x6,binarized

32x32

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Quantum-assistedunsupervisedlearningondigits

OptDigits Datasets

Dataset:OpticalRecognitionofHandwrittenDigits(OptDigits)

Page 13: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Quantum-assistedunsupervisedlearningondigits

46fully-connectedlogical(visible)variables

940physicalqubits

- Aretheresultsfromthistrainingon940qubitexperimentmeaningful?

- Isthemodelcapableofgeneratingdigits?

42forpixels+4toone-hotencodetheclass(onlydigits1-4)

Overcomingthecurseoflimitedconnectivity inhardware.

Min.CL=12,Max.CL=28

Page 14: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Quantum-assistedunsupervisedlearningondigits

(quantum) machine

Human

Humanor(quantum)machine?(Turingtest)

Dataset:OpticalRecognitionofHandwrittenDigits(OptDigits)

Resultsfromexperimentsusing940qubits,withoutpost-processing.Thehardware-embeddedmodelrepresentsa46nodefullyconnectedgraph.

Page 15: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Anear-termapproachforquantum-enhancedmachinelearningChallengesofthehybridapproach:

Benedettietal.arXiv:1609.02542

Fullyvisiblemodels

Visibleunits

- Robustnesstonoise,intrinsiccontrolerrors,andtodeviationsfromsamplingmodel(e.g.,Boltzmann)

- Curseoflimitedconnectivity – parametersetting

Howaboutlargecomplexdatasetswithcontinuousvariables?Allpreviousfailtodothat(fullyquantumandhybridhere)

- Needtosolveclassical-quantummodelmismatch

Training Method: Stochastic gradient ascent

Benedettietal.Phys.Rev.A94,022308(2016)

Classical Quantum-Teff?

NoprogressinfiveyearssinceQAsamplingwasproposedasapromissingappplication.

Visibleunits Hiddenunits

Page 16: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Perspectiveonquantum-enhancedmachinelearning

Compresseddata

Rawinputdata

Measurement

Hiddenlayers

Inference

Qua

ntum

processing

Classicalpre-a

ndpost-p

rocessing

Visibleunits Hiddenunits Qubits

Trainingsamples

• Newhybridproposalthatworksdirectlyonalow-dimensionalrepresentationofthedata.

Page 17: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Perspectiveonquantum-enhancedmachinelearning

Compresseddata

i~d⇢✓(t)dt

= [H✓, ⇢✓]i~d⇢✓(t)

dt= [H✓, ⇢✓]

Rawinputdata

Quantumsampling

Measurement

Hiddenlayers

ClassicalgenerationorreconstructionofdataIn

ference

Qua

ntum

processing

Classicalpre-a

ndpost-p

rocessing

Visibleunits Hiddenunits Qubits

Trainingsamples

Generatedsamples

• Newhybridproposalthatworksdirectlyonalow-dimensionalrepresentationofthedata.

Page 18: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Perspectiveonquantum-enhancedmachinelearning

Compresseddata

i~d⇢✓(t)dt

= [H✓, ⇢✓]i~d⇢✓(t)

dt= [H✓, ⇢✓]

Rawinputdata

Quantumsampling

Measurement

Hiddenlayers

ClassicalgenerationorreconstructionofdataIn

ference

Qua

ntum

processing

Classicalpre-a

ndpost-p

rocessing

Visibleunits Hiddenunits Qubits

Corruptedimage

Reconstructedimage

• Newhybridproposalthatworksdirectlyonalow-dimensionalrepresentationofthedata.

Benedetti,Realpe-Gomez,andPerdomo-Ortiz.Quantum-assistedHelmholtzmachines:Aquantum-classicaldeeplearningframeworkforindustrialdatasetsinnear-termdevices.arXiv:1708.09784 (2017).

Page 19: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

ExperimentalimplementationoftheQAHM

Experimentsusing1644qubits (nofurtherpostprocessing!)

Benedetti,Realpe-Gomez,andPerdomo-Ortiz.Quantum-assistedHelmholtzmachines:Aquantum-classicaldeeplearningframeworkforindustrialdatasetsinnear-termdevices.arXiv:1708.09784 (2017).

Max. CL = 43

Page 20: Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers Alejandro Perdomo-Ortiz,1,2,3,

Opportunities and challenges for quantum-assisted machine learning in near-termquantum computers

Alejandro Perdomo-Ortiz,1, 2, 3, ⇤ Marcello Benedetti,1, 3 John Realpe-Gomez,1, 4, 5 and Rupak Biswas6

1Quantum Artificial Intelligence Lab., NASA Ames Research Center, Mo↵ett Field, CA 94035, USA2USRA Research Institute for Advanced Computer Science (RIACS), 615 National, Mountain View CA 94043, USA

3Department of Computer Science, University College London, WC1E 6BT London, United Kingdom4SGT Inc., 7701 Greenbelt Rd., Suite 400, Greenbelt, MD 20770, USA

5Instituto de Matematicas Aplicadas, Universidad de Cartagena, Bolıvar 130001, Colombia6Exploration Technology Directorate, NASA Ames Research Center, Mo↵ett Field, CA 94035, USA

[Abstract here]

I. INTRODUCTION

With the advent of quantum computing technologiesnearing the era of commercialization and of quantumsupremacy [? ], it is a pressing task to think of potentialapplications that might benefit from these devices. Ma-chine learning stands out as a powerful statistical frame-work that have allowed for the solution of problems wheredeterministic algorithms are hard to develop. Examplesof such algorithms include image and voice recognition,medical applications [Marc: mention here other selectedkick ass app for ML]. The development of quantum algo-rithms that can assist or replace in it entirety the classi-cal ML routine is an ongoing e↵ort that has attracted alot of interest in the scientific quantum information com-munity. [cite all or most representative work here, e.g.,Dorband et al :’D]

Although the focus has been on tasks such as classifi-cation [cite Rebentrost, etc, etc], linear regression [cite],Gaussian models [cite Fitzsimmons] [find other represen-tative examples] corresponding to the most widely usednowadays by machine learning practitioners, we do notforesee these ones would be important for near-term usesof quantum computers. The same reasons that makethese techniques so popular, e.g., their scalability andalgorithmic e�ciency in tackling huge datasets, makesthese techniques less appealing to become top candi-dates as killer application in quantum machine learningwith devices in the range of 100-1000 qubits. In otherwords, to reach interesting industrial scale applicationsit would be required at least millions or even billionsof qubits before one make them competitive with classi-cal e�cient algorithms. This is even under the assump-tion of a quadratic or exponential speedup, which be-comes a mute advantage when dealing with real-worlddatasets and with the quantum devices to come in thenext decades nearing the 1000s of qubits regime. Only agame changer, as elaborated later on this perspective, forexample by introducing hybrid algorithms might be ableto also make a dent in speeding up such routine tasks.

In our perspective here, we propose and emphasize two

⇤Correspondence: [email protected]

approaches to maximize the possibilities of finding killerapplications on near-term quantum computers:

(i) Focus on problems that are currently hard and in-tractable for the ML community: For example,fully generative models, unsupervised and semi-supervised learning as described in Sec. II.

(ii) Focus on hybrid quantum algorithms that can beeasily integrated in the intractable step of the MLalgorithmic pipeline, as described in Sec. IV.

Each one of these tasks have their own challenges andsignificant work need to be done towards having experi-mental implementations on available quantum hardware(see e.g., [Benedetti1, Benedetti2]. Based on our pastexperience in implementing quantum-assisted ML algo-rithms on existing quantum hardware devices, we providehere some insights into the main challenges ahead in de-veloping such opportunities for QML. Although the focushere is on implementations on quantum annealers, we at-tempt to provide parallel insights in other computationalparadigms such as the gate model of quantum computa-tion. The guidance on which problems to be tackled isguided by our expertise in ML and by the advice fromexperts in the ML community.In Sec. II we present examples of domains in ML we

believe o↵er vlable opportunities for near-term quantumcomputers. In Sec. III we present the challenges ahead ofsuch implementations in real hardware, while in Sec. IVwe provide some advice on potential solutions to over-coming these challenges towards such implementations.In Sec. ?? we summarize our work.

II. OPPORTUNITIES IN QML

a. Scenarios where labeled data is scarce: Our fo-cus is on unsupervised learning techniques that canextract salient spatiotemporal features from unlabeleddata. This is important because one of the central as-pects of science is the discovery of unknown patterns;nobody tells scientists which patterns they should lookfor. This also serves as a pre-training phase that can sub-stantially reduce the amount of labeled data needed for

- Opportunities: EmphasisinmovingfrompopularMLtonot-so-popularbutstillhighlyvalueMLapplications.Example:Fromdiscriminativemodelstomorepowerfulgenerativemodels.Also,classicaldatasetswithintrinsicquantumcorrelations.

- Challenges: Limitedqubit-qubit connectivity,limitedprecision,intrinsiccontrolerrors,digitalrepresentation,classical-quantumfeedback(incaseofhybrid).

- Proposeddirections:Emphasisonhybridquantum-classicalalgorithms.Newapproachcapableoftacklinglargecomplexdatasetsinmachinelearning.

arXiv:1708.09757.(2017).ToappearintheQuantumScienceandTechnology(QST)invitedspecialissueon“Whatwouldyoudowitha1000qubitdevice?”

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https://usra-openhire.silkroad.com/epostings/index.cfm?fuseaction=app.jobInfo&version=1&jobid=629

OpportunitiesatNASAQuantumAILab.(NASAQuAIL)atdifferentlevels:internships,postdoc,orResearchScientist.

Fordetails,pleasecontact:EleanorRieffel: NASAQuAIL Lead,or,AlejandroPerdomo-Ortiz:[email protected],[email protected]

Jobadvertisement

NASAAmesResearchCenter

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