NASA:Quantum Machine Learning

Opportunities and challenges in quantum-enhanced machine learning in near-term quantum computers

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

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?”

QUBITS D-wave User Group 2017 National Harbor, MD, September 28, 2017 D-Wave System Capability 1) As a discrete optimization solver: Potential NASA applications: - planning Given {hj, Jij}, find {sk = ± 1} NP-hard - scheduling that minimizes problem - fault diagnosis - graph analysis N N - communication networks, etc. ⇠(s1,...,sN )= hjsj + Jijsisj QUBO: Quadratic Unconstrained j=1 i,j E X X2 Binary Optimization (Ising model in physics jargon).

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

P exp[ ⇠(s ,...,s )/T ] Computationally Boltzman / 1 N eff bottleneck

Early work: Our work: Benedetti et al. PRA 94, 022308 (2016) Bian et al. 2010. The Ising model: teaching an old problem new tricks. • We provide a robust algorithm to estimate the effective temperature of problem instances in quantum annealers. Follow-up work: Raymond et al. Global warming: Temperature estimation in annealers. • Algorithm uses the same samples that will be used for the estimation of Frontiers in ICT, 3, 23 (2016). the gradient

RBM Widely used in Hidden units Potential NASA applications: unsupervised - machine leaning (e.g., training learning Visible units of deep-learning networks) Unsupervised learning (generative models)

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

MODEL P ( Image )

Learning algorithm

NO LABELS

DATASET Unsupervised learning (generative models)

Learn the “best” model distribution that Example application: can generate the same kind of data Image reconstruction

MODEL P ( Image ) Reconstructed image

Learning algorithm LEARNED MODEL P ( Image )

NO LABELS

Damaged image

DATASET Supervised learning (discriminative models)

Learn the “best” model that can Example application: perform a specific task Image recognition

MODEL Predicted P ( Label | Image ) label 61

Learning algorithm LEARNED MODEL Labels P ( Label | Image )

26624 98 66 175

Image to be recognized

DATASET A near-term approach for quantum-enhanced machine learning State-of-the-art QML - Most previous proposed work have - Need for qRAM (case of most gate- highly optimized powerful classical based proposal). counterparts (e.g., on - Qubits represent visible units; issue discriminative/classification tasks) for case of large datasets

Lesson 1: Move to intractable problems of interest to ML experts (e.g., generative models in unsupervised learning).

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

Bayesian Deep Probabilistic Others... inference learning programming

Hypothesis: intractable sampling problems enhanced by quantum sampling A near-term approach for quantum-enhanced machine learning

Lesson 2: Need for novel hybrid approaches.

Challenges solved:

PREDICTIONS Benedetti, et al. Estimation of effective temperatures in quantum annealers for t F [ P(s|Θ ) ] sampling applications: A case study with possible applications in deep learning. PRA 94, 022308 (2016). LEARNING HARD TO COMPUTE Stochastic gradient descent Benedetti, et al. Quantum-assisted Estimation assisted by sampling learning of graphical models with t+1 t t Θ = Θ + G [ P(s|Θ ) ] from quantum computer arbitrary pairwise connectivity. arXiv:1609.02542 (2016).

Ex.: Restricted Boltzmann Benedetti, et al. Quantum-assisted DATA Machines (RBM) Helmholtz machines: A quantum-classical 1 D deep learning framework for industrial s = {s ,…, s } RBM Hidden units, u datasets in near-term devices. arXiv:1708.09784 (2017). Computationally Visible units, v bottleneck Perdomo-Ortiz, et al. Opportunities and Where, Widely used in E(v,u ✓)/T e | eff unsupervised Challenges in Quantum-Assisted Machine viuj p(v,u) p(v, u)= h i Z(✓) learning Learning in Near-term Quantum Computer. arXiv:1708.09757. (2017). A near-term approach for quantum-enhanced machine learning

Challenges of the hybrid approach:

- Need to solve classical-quantum model mismatch

Training Method: Stochastic gradient ascent @ ln (✓ v) L | viuj data viuj model @Jij /h i h i v D X2 Classical - Quantum Teff?

Benedetti et al . Phys. Rev. A 94, 022308 (2016)

Visible units Hidden units

No significant progress in 2010-2015 for generative modeling and QA sampling. 6 (a) 7 8

av L 9 10 With Bias Correction Without Bias Correction 11 0 200 400 600 800 1000

6 (b) 7 8

av L 9 10 With Importance Sampling Without Importance Sampling A near-term approach for quantum-enhanced machine learning 11 0 200 400 600 800 1000 Resolving model mismatch allows for restarting from classical preprocessing

6 (c) QuALe @ TDW2X =0.033 with Restart 7 QuALe @ Te↵ with Restart 8 CD-1

av L 9 10 11 0 100 200 300 400 500 iteration

Benedetti et al . Phys. Rev. A 94, 022308 (2016) A near-term approach for quantum-enhanced machine learning

Challenges of the hybrid approach:

- Need to solve classical-quantum model - Robustness to noise, Fully visible models mismatch intrinsic control errors, and to deviations from Training Method: Stochastic gradient ascent sampling model (e.g., @ ln (✓ v) Boltzmann) L | viuj data viuj model @Jij /h i h i v D Visible units X2 - Curse of limited connectivity – parameter Classical Quantum - setting Benedetti et al. Teff? arXiv:1609.02542

Benedetti et al . Phys. Rev. A 94, 022308 (2016)

Visible units Hidden units

No significant progress in 2010-2015 for generative modeling and QA sampling. Quantum-assisted unsupervised learning on digits

OptDigits Datasets

32x32

8x8 7x6 7x6, binarized

Dataset: Optical Recognition of Handwritten Digits (OptDigits) Quantum-assisted unsupervised learning on digits

OptDigits Datasets

Dataset: Optical Recognition of Handwritten Digits (OptDigits) Quantum-assisted unsupervised learning on digits

Overcoming the curse of limited connectivity in hardware.

46 fully-connected logical (visible) variables

42 for pixels + 4 to one-hot encode the class (only digits 1-4)

- Are the results from this training on 940 qubit experiment meaningful? - Is the model capable of generating digits?

Min. CL =12, Max. CL = 28 940 physical qubits Quantum-assisted unsupervised learning on digits

Human or (quantum) machine? (Turing test)

Human

(quantum) machine

Dataset: Optical Recognition of Handwritten Digits (OptDigits)

Results from experiments using 940 qubits, without post-processing. The hardware-embedded model represents a 46 node fully connected graph. A near-term approach for quantum-enhanced machine learning Challenges of the hybrid approach:

- Curse of limited Visible units connectivity – parameter Classical - Quantum setting Benedetti et al. T ? eff arXiv:1609.02542

Benedetti et al . Phys. Rev. A 94, 022308 (2016) How about large complex datasets Visible units Hidden units with continuous variables? All previous fail to do that (fully No progress in five years since QA sampling was proposed as a quantum and hybrid here) promissing appplication. Perspective on quantum-enhanced machine learning

• New hybrid proposal that works directly on a low-dimensional representation of the data. Quantum processing

Compressed data

Hidden layers processing - Inference and post -

Raw input data Training

Classical pre samples

Visible units Hidden units Qubits Measurement Perspective on quantum-enhanced machine learning

• New hybrid proposal that works directly on a low-dimensional representation of the data.

d⇢ˆ (t) Quantum sampling i ✓ =[Hˆ , ⇢ˆ ] ~ ✓ ✓ d⇢ˆ✓(t) ˆ dt i~ =[H✓, ⇢ˆ✓] dt ✓ Quantum processing

Compressed data Classical Hidden generation or layers reconstruction processing - of data Inference and post -

Raw input data Training Generated

Classical pre samples samples Visible units Hidden units Qubits Measurement Perspective on quantum-enhanced machine learning

• New hybrid proposal that works directly on a low-dimensional representation of the data.

d⇢ˆ (t) Quantum sampling i ✓ =[Hˆ , ⇢ˆ ] ~ ✓ ✓ d⇢ˆ✓(t) ˆ dt i~ =[H✓, ⇢ˆ✓] dt ✓ Quantum processing

Compressed data Classical Hidden generation or layers reconstruction processing - of data Inference and post -

Raw input data Corrupted Reconstructed

Classical pre image image

Visible units Hidden units Qubits Measurement

Benedetti, Realpe-Gomez, and Perdomo-Ortiz. Quantum-assisted Helmholtz machines: A quantum-classical deep learning framework for industrial datasets in near-term devices. arXiv:1708.09784 (2017). Experimental implementation of the QAHM

Experiments using 1644 qubits (no further postprocessing!) Max. CL = 43

1, 2, 3, 1, 3 1, 4, 5 6 Alejandro Perdomo-Ortiz, ⇤ Marcello Benedetti, John Realpe-Gómez, and Rupak Biswas 1Quantum Artificial Intelligence Lab., NASA Ames Research Center, Mo↵ett Field, CA 94035, USA 2USRA 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 Kingdom 4SGT Inc., 7701 Greenbelt Rd., Suite 400, Greenbelt, MD 20770, USA 5Instituto de Matemáticas Aplicadas, Universidad de Cartagena, Bol´ıvar130001, Colombia 6Exploration Technology Directorate, NASA Ames Research Center, Mo↵ett Field, CA 94035, USA [Abstract here]

I. INTRODUCTION approaches to maximize the possibilities of finding killer applications on near-term quantum computers: With the advent of quantum computing technologies nearing- theOpportunities: era of commercializationEmphasis in moving from popular ML to not and of quantum (i) Focus on-so problems-popular but still highly value that are currently hard and in- supremacy [? ], it is a pressing task to think of potential tractable for the ML community: For example, ML applications. Example: From discriminative models to more powerful generative models. fully generative models, unsupervised and semi- applicationsAlso, classical datasets with intrinsic quantum correlations. that might benefit from these devices. Ma- chine learning stands out as a powerful statistical frame- supervised learning as described in Sec. II. work that have allowed for the solution of problems where deterministic- Challenges: algorithmsLimited are hardqubit to- develop.qubit connectivity, limited precision, intrinsic control errors, digital Examples (ii) Focus on hybrid quantum algorithms that can be of such algorithmsrepresentation, classical include image and-quantum feedback (in case of hybrid). voice recognition, easily integrated in the intractable step of the ML medical applications [Marc: mention here other selected algorithmic pipeline, as described in Sec. IV. kick ass app for ML]. The development of quantum algorithms- thatProposed directions: can assist or replace inEmphasis on hybrid quantum it entirety the classi- Each-classical algorithms. New approach one of these tasks have their own challenges and cal ML routinecapable of tackling large complex datasets in machine learning. is an ongoing e↵ort that has attracted a significant work need to be done towards having experi- lot of interest in the scientific quantum information com- mental implementations on available quantum hardware munity. [cite allarXiv:1708.09757 or most representative. (2017). workTo appear in the Quantum Science and Technology (QST here, e.g., (see e.g., [Benedetti1, Benedetti2]. Based) on our past experience in implementing quantum-assisted ML algo- Dorband et al :’D] invited special issue on “What would you do with a 1000 qubit device?” Although the focus has been on tasks such as classifi- rithms on existing quantum hardware devices, we provide cation [cite Rebentrost, etc, etc], linear regression [cite], here some insights into the main challenges ahead in de- Gaussian models [cite Fitzsimmons] [find other represen- veloping such opportunities for QML. Although the focus tative examples] corresponding to the most widely used here is on implementations on quantum annealers, we at- nowadays by machine learning practitioners, we do not tempt to provide parallel insights in other computational foresee these ones would be important for near-term uses paradigms such as the gate model of quantum computa- of quantum computers. The same reasons that make tion. The guidance on which problems to be tackled is these techniques so popular, e.g., their scalability and guided by our expertise in ML and by the advice from algorithmic eciency in tackling huge datasets, makes experts in the ML community. these techniques less appealing to become top candi- In Sec. II we present examples of domains in ML we dates as killer application in quantum machine learning believe o↵er vlable opportunities for near-term quantum with devices in the range of 100-1000 qubits. In other computers. In Sec. III we present the challenges ahead of words, to reach interesting industrial scale applications such implementations in real hardware, while in Sec. IV it would be required at least millions or even billions we provide some advice on potential solutions to over- of qubits before one make them competitive with classi- coming these challenges towards such implementations. cal ecient algorithms. This is even under the assump- In Sec. ?? we summarize our work. tion of a quadratic or exponential speedup, which be- comes a mute advantage when dealing with real-world datasets and with the quantum devices to come in the II. OPPORTUNITIES IN QML next decades nearing the 1000s of qubits regime. Only a game changer, as elaborated later on this perspective, for a. Scenarios where labeled data is scarce: Our fo- example by introducing hybrid algorithms might be able cus is on unsupervised learning techniques that can to also make a dent in speeding up such routine tasks. extract salient spatiotemporal features from unlabeled In our perspective here, we propose and emphasize two data. 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 look for. This also serves as a pre-training phase that can sub- ⇤ Correspondence: [email protected] stantially reduce the amount of labeled data needed for Job advertisement

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Opportunities at NASA Quantum AI Lab. (NASA QuAIL) at different levels: internships, postdoc, or Research Scientist.

For details, please contact: Eleanor Rieffel: NASA QuAIL Lead, or, Alejandro Perdomo-Ortiz: Quantum Machine Learning Lead. [email protected], [email protected] https://usra-openhire.silkroad.com/epostings/index.cfm?fuseaction=app.jobInfo&version=1&jobid=629 Support slides