Topics in Quantum Machine Learning Vedran Dunjko - PowerPoint PPT Presentation

Topics in Quantum Machine Learning Vedran Dunjko v.dunjko@liacs.leidenuniv.nl 1

Q uantum M achine L earning (QML) Q uantum I nformation M achine L earning/ AI P rocessing ( QIP ) (ML/AI) ML → QIP (quantum-applied ML) [’74] QIP → ML (quantum-enhanced ML) [‘94] QIP ↭ ML (quantum-generalized learning) [‘00] ML-insipred QM/QIP Physics inspired ML/AI 2

Machine learning is not one thing. AI is not even a few things. unsupervised learning big data analysis ML supervised learning generative models deep learning sequential decision online learning non-parametric theory learning reinforcement learning computational learning theory control theory parametric learning statistical learning non-convex AI local search optimization Symbolic AI 3

Quantum-enhanced ML is even more things big data analysis unsupervised learning ML Quantum linear algebra supervised learning generative models Shallow quantum deep learning online learning sequential circuits decision non-parametric reinforcement Quantum oracle theory learning learning identification Adiabatic QC/ parametric learning Quantum control theory non-convex computational learning theory Quantum optimization COLT optimization Quantum statistical learning local search AI walks & search Symbolic AI 4

Quantum-enhanced ML is even more things big data analysis unsupervised learning ML Quantum linear algebra supervised learning generative models Shallow quantum deep learning online learning sequential circuits decision non-parametric reinforcement theory learning learning parametric learning Adiabatic QC/ control theory non-convex computational learning theory Quantum optimization optimization statistical learning local search AI Symbolic AI 5

And then there’s Quantum-applied ML! QKD parameter phase control Hybrid computation diagrams (AI) Quantum network QIP optimization order NISQ optimization, Efficient parameters QAOA & VQE decoders Adaptive error Ground state correction Circuit Ansatz control and synthesis optimization of qubits Metrology Q. Phys Experiment synthesis high-energy 6

Unsupervised learning g n i n r a e QKD parameter l t n e m phase e c r control o f Hybrid computation n i e diagrams R g n i n r (AI) a e l d e Quantum network s QIP i v r e p u S optimization order R NISQ optimization, e Efficient i parameters n QAOA & VQE f S o decoders u r c p e e m r l a Adaptive error r g Ground state v u n e e i n N i r Circuit a s n e l correction t n Ansatz e t e control and s m k e r d l synthesis o c r w e o t f e n n l a i e optimization of e R g r n a i n n r a e r qubits i l d n n Metrology e s Experiment i v i g r n e p u S g synthesis Q. Phys g n i high-energy n r a e l d e s i v r e p u S 7

What is machine learning 8

Machine Learning: the WHAT ? or -generative models -clustering (discriminative) Learning P(labels|data) given -feature extraction samples from P(data,labels) Learning structure in P(data) (also regression) give samples from P(data) 9

Machine Learning: the WHAT Beyond data: reinforcement learning T ( s | s 0 , a ) 10

Also: MIT technology review breakthrough technology of 2017 [AlphaGo anyone?] 11

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Using RL in Real Life Navigating a city… https://sites.google.com/view/streetlearn P. Mirowski et. al, Learning to Navigate in Cities Without a Map , arXiv:1804.00168 13

Machine Learning: the HOW output hypothesis h on Data x Labels approximating P(labels|data) In practice model 
 Optimizer parameters θ estimate error on sample (dataset) 14

Support vector machines separating hyperplane.. 15

Support vector machines separating hyperplane.. …in higher-dimensional feature space Still (algebraic) optimization over hyperplane and feature function parameters…. 16

Machine Learning: the HOW Learning structure in P(data) give samples from P(data) 17

Machine Learning: the HOW output: output: hypothesis h on Data x Labels hypothesis h on Data approximating P(labels|data) “ approximating” P(data) Reinforcement learning output: policy π on Actions x States 18

Supervised learning Unsupervised learning (learning how to label datapoints, (learning a distribution, learning how to approximate a function, generate. properties from samples, how to classify ) feature extraction & dim. reduction ) Reinforcement learning (learning behavior , policy , or optimal control )

That is all ML we need for now What about quantum computers? 20

Quantum computers… …and computer science …and physics -likely can efficiently compute more things - manipulate registers of than classical computers (factoring) 2-level systems (qubits) e.g. factor numbers, or generate complex distributions -even if QC is “shallow” -full description: n qubits → 2 n dimensional vector - manipulation : acting locally ( gates ) …and reality cca 50 qubit special-purpose all-purpose quantum annealers Banana noisy for scale 21

Quantum computers… …and computer science …and physics -can compute things likely beyond BPP (factoring) - manipulate registers of -can produce distributions which are hard-to-simulate 2-level systems (qubits) for classical computers (unless PH collapses ) -full description: -even if QC is “shallow” n qubits → 2 n dimensional vector …and reality cca 50 qubit special-purpose all-purpose quantum annealers Banana noisy for scale 22

8 Quantum-enhanced supervised learning: the quantum pipeline a) The optimization bottleneck b) Big data & comp. complexity c) Machine learning Models 23

Quantum-enhanced supervised learning: the quantum pipeline a) The optimization bottleneck — quantum annealers b) Big data & comp. complexity — universal QC and Q. databases — restricted (shallow) architectures c) Machine learning Models 24

Quantum-enhanced supervised learning: the quantum pipeline a) The optimization bottleneck — quantum annealers b) Big data & comp. complexity — universal QC and Q. databases — restricted (shallow) architectures c) Machine learning Models 25

The optimization bottleneck H ( s ) = sH initial + (1 − s ) H target ; s ( time ) • Finding ground states of Hamiltonians via adiabatic evolution 
 • Very generic optimization problem: argmin | ψ i h ψ | H | ψ i

QeML is even more things big data analysis unsupervised learning ML Quantum linear algebra supervised learning generative models Shallow quantum deep learning online learning sequential circuits decision non-parametric reinforcement theory learning learning parametric learning Adiabatic QC/ control theory non-convex computational learning theory Quantum optimization optimization Quantum statistical learning local search walks & search AI Symbolic AI 27

Quantum-enhanced supervised learning: the quantum pipeline a) The optimization bottleneck — quantum annealers b) Big data & comp. complexity — universal QC and Q. databases — restricted (shallow) architectures c) Machine learning Models 28

Precursors of Quantum Big Data Exponential data? Much of data analysis is linear-algebra: + regression = Moore-Penrose PCA = SVD… 29

Enter quantum linear algebra amplitude encoding exp(n) amplitudes interpret QM as linear algebra verbatim R N 3 x = ( x i ) i in n qubits ↓ | ψ i / P N state vector ↔ (data) vector i =1 x i | i i density matrices block encoding Hamiltonians ↔ linear maps unitaries  �  �  � A B A ψ ψ U | 0 i | ψ i = = | 0 i A | ψ i + | 0 i C | ψ i = C D C ψ 0 projective ↔ inner products measurements functions of operators (swap tests) f ( A ) | ψ i = α 0 | ψ i + α 1 A | ψ i + α 0 A 2 | ψ i · · · ⇡ · · · ⇡ A − 1 | ψ i prepare states expressible as linear-algebraic inner products manipulations of data-vectors in polylog(N) P (0) ψ = | h 0 | ψ i | 2 (when other quantities are well behaved) Phys. Rev. Lett. 15 ,. 103, 250502 (2009) arXiv:1806.01838 30

If this worked literally…this would make us INFORMATION GODS. Prediction: 44 zettabytes by 2020. If all data is floats, this is 5.5x10 21 float values

If this worked literally…this would make us INFORMATION GODS. Prediction: 44 zettabytes by 2020. If all data is floats, this is 5.5x10 21 float values … can be stored in state of 73 qubits (ions, photons….)

Clearly there is a catch. Many of them.

Timeline We made it so efficient… that sometimes we don’t need QCs!! First efficient end-to-end Machine learning Data-robustness Linear scenario applications & implies system q. efficiency Improvements Quantum solving database QLA, smoothed analysis, De-quantization of Quantum low-rank systems Recommender Optimal Systems Regression, QLS PCA, SVM HHL Pattern QRAM recognition on a QC { 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 3 9 9 2 3 8 4 6 8 ?