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: - 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., Boltzmann) - 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 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). Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers 1, 2, 3, 1, 3 1, 4, 5 6 Alejandro Perdomo-Ortiz, ⇤ Marcello Benedetti, John Realpe-G´omez, and Rupak Biswas 1Quantum Artificial Intelligence Lab., NASA Ames Research Center, Mo↵ett Field, CA 94035,