from quantum machine learning to quantum aiblogs.esa.int/philab/files/2019/04/vdunjko_leiden.pdf ·...
TRANSCRIPT
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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
Quantum Information Processing (QIP)Machine Learning/AI
(ML/AI)
Quantum Machine Learning (QML)
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3
Machine learning is not one thing. AI is not even a few things.
AI
supervised learning
unsupervised learning
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory
non-convex optimization
sequential decision theory
MLbig data analysis
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QeML is even more things
AI
supervised learning
unsupervised learning
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
sequential decision theory
MLbig data analysis
Quantum linear algebra
Shallow quantum circuits
Quantum oracle identification
Quantum walks & search
Adiabatic QC/ Quantum optimization
Quantum COLT
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5
QeML is even more things
AI
supervised learning
unsupervised learning
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
sequential decision theory
MLbig data analysis
Quantum linear algebra
Shallow quantum circuits
Quantum walks & search
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Learning P(labels|data) given samples from P(data,labels)
-generative models -clustering (discriminative) -feature extraction
Machine Learning: the WHAT
or
Sudo is this a cat?Sudo make me a cat. Sudo what is a cat!?
Learning structure in P(data) give samples from P(data)
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Machine Learning: the HOW
output hypothesis h on Data x Labels approximating P(labels|data)
output hypothesis h on Data “approximating” P(data)
model parameters θ
estimate error
on sample (dataset)
OptimizerIn practice
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What about quantum computers?
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-manipulate registers of 2-level systems (qubits)
-full description:
n qubits → 2n dimensional vector
-likely can efficiently compute more things than classical computers (factoring) e.g. factor numbers, or generate complex distributions
-even if QC is “shallow”
Banana for scale
cca 50 qubit all-purpose noisy
…and physics …and computer science
…and reality
Quantum computers…
-manipulation: acting locally (gates)
special-purpose quantum annealers
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Quantum computers…
…and physics …and computer science
…and reality
-can compute things likely beyond BPP (factoring)
-can produce distributions which are hard-to-simulate for classical computers (unless PH collapses)
-even if QC is “shallow”
Banana for scale
special-purpose quantum annealers
cca 50 qubit all-purpose noisy
-manipulate registers of 2-level systems (qubits)
-full description:
n qubits → 2n dimensional vector
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Bottlenecks of ML and the quantum pipeline
a) The optimization bottleneck b) Big data & comp. complexity c) Machine learning Models
8
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Bottlenecks of ML and the quantum pipeline
a) The optimization bottleneck — quantum annealers b) Big data & comp. complexity — universal QC and Q. databasesc) Machine learning Models — restricted (shallow) architectures
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Bottlenecks of ML and the quantum pipeline
a) The optimization bottleneck — quantum annealers b) Big data & comp. complexity — universal QC and Q. databasesc) Machine learning Models — restricted (shallow) architectures
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Exponential data?
+Much of data analysis
is linear-algebra:
regression = Moore-Penrose PCA = SVD…
Precursors of Quantum Big Data
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%
AI
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
sequential decision theory
ML Quantum linear algebra
Shallow quantum circuits
Adiabatic QC/ Quantum optimization
Quantum oracle identification
Quantum walks
big data analysis
supervised learning
unsupervised learning
6
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Enter quantum linear algebra
| i /PN
i=1 xi|ii
R
N 3 x = (xi)i#
f(A)| i = ↵0| i+ ↵1A| i+ ↵0A2| i · · · ⇡ A�1| i
U |0i| i =A BC D
� 0
�=
A C
�= |0iA| i+ |0iC| i
f(A)| i = ↵0| i+ ↵1A| i+ ↵0A2| i · · · ⇡ A�1| i
amplitude encoding
block encoding
functions of operators
Phys. Rev. Lett. 15,. 103, 250502 (2009) arXiv:1806.01838
-n qubits ↔ 2n dimensional vector
-compute evolution = linear algebra
-so… evolution of quantum systems *does* linear algebra
-with exponentially large matrices!inner productsP (0) = |h0| i|2
exp(n) amplitudes
in n qubits
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Prediction: 44 zettabytes by 2020.
If all data is floats, this is 5.5x1021 float values
If this worked literally…this would make us INFORMATION GODS.
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Prediction: 44 zettabytes by 2020.
If all data is floats, this is 5.5x1021 float values
… can be stored in state of 73 qubits (ions, photons….)
If this worked literally…this would make us INFORMATION GODS.
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Timeline
20032008
20092012
20142013
20162018
Pattern recognition on a QC
QRAMHHL
Regression, PCA, SVM
Optimal QLS
Quantum Recommender Systems
QLA, smoothed analysis, De-quantization of low-rank systems
2019?
{
Quantum database
Linear system solving
Machine learning applications & Improvements
First efficient end-to-end scenario
We made it so efficient… that sometimes
we don’t need QCs!!
Data-robustness implies
q. efficiency
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-Quantum works with full-rank transforms (e.g. Fourier for series) -polynomial advantage (up to 16 degree difference at the moment) -error scaling: exponential precision v.s. poly (in-)precision
-exponentially efficient processing given suitable databases
Quantum and classical
Summary of quantum (inspired) “big data”
Quantum advantages over classical
The “bad”-not an inexhaustible source of exponential quantum advantage
15
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Bottlenecks of ML and the quantum pipeline
a) The optimization bottleneck — quantum annealers
b) Big data & comp. complexity — universal QC and Q. databasesc) Machine learning Models — restricted (shallow) architectures
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(Quantum) Machine learning Models
Improving ML == speeding up algorithms… or is it?
model parameters θ
estimate error
on sample (dataset)
Optimizer
“Machine learning”
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24
Machine learning Models matter!
Image: 10.1016/j.compstruct.2018.03.007
best fit v.s. “generalization performance” or classifying well beyond the training set
Data:
Models:
Not all models (+training algo) are born equal (for real datasets)…
Challenge:squeek
or meow?
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big data analysis unsupervised learning
25
AI
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
sequential decision theory
ML Quantum linear algebra
Shallow quantum circuits
Quantum oracle identification
Quantum walks
supervised learning
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Machine learning Models
model parameters θ
estimate error
on sample (dataset)
Optimizer
“Machine learning”
family of functions. if it’s “good”, we can generalize well
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model parameters θ
estimate error
on sample (dataset)
Optimizer
How about “shallow quantum circuits”? -instead neural network, train a QC! -related to ideas from q. condensed-matter physics (VQE)
=
=
=
=
=
Quantum Machine learning Models
“quantum kernel methods”
Phys. Rev. Lett. 122, 040504 2019 Nature 567, 209–212 (2019) (c.f. Elizabeth Behrman in ‘90s)
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Quantum Machine learning Models“quantum kernel methods”
The good - near term architectures - seems to be robust
(noise not inherently critical!) - possibly very expressive
The neutral - many parameters - model advantages less clear (contrast to variational methods!)
The bad - barren plateaus (also in DNN)
(x1 _ x4 _ x10)| {z } (x1 _ x4 _ x10)| {z }
=
=
=
=
=
|�(✓in, ✓class)i
✓class✓in(x)
{(x, label)i}
estimate error
on sample (dataset)
Optimizer
(fidu
cial
)
Phys. Rev. Lett. 122, 040504 2019 Nature 567, 209–212 (2019)
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A hope… killer app for noisy QCs?
ML good for dealing with noise (in *data*)… Can QML deal with its own noise (in *process*)?
18
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Beyond ML?
big data analysis unsupervised learning
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
ML Quantum linear algebra
Shallow quantum circuits
Quantum oracle identification
Quantum walks
supervised learning
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big data analysis unsupervised learning
31
AI
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
sequential decision theory
ML Quantum linear algebra
Shallow quantum circuits
Adiabatic QC/ Quantum optimization
Quantum oracle identification
Quantum walks
supervised learning
Quantum-enhanced reinforcement learning
c.f. Briegel
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big data analysis unsupervised learning
32
AI
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
sequential decision theory
ML Quantum linear algebra
Shallow quantum circuits
Adiabatic QC/ Quantum optimization
Quantum oracle identification
Quantum walks
supervised learning
Towards good-old-fashioned-AI
-planning -(symbolic) reasoning -automated proving -logic
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3
Find a proof of Riemann’s hypothesis
with less than a million lines(if it exists)?
Optimal packingShortest tours
Traffic flow optimization
finding *good* (not worst case!) solutions to this is central to AI
RL and ML
f(x1, . . . , xn) = C1 ^ C2 ^ · · ·Ck ^ · · ·CL
Ck = (u _ v _ w), u, v, w 2 {x1, . . . , xn} [ {x̄1, . . . , x̄n}
f(x1, . . . , xn) = (x1 _ x10 _ x̄51) ^ (x̄3 _ x̄10 _ x̄11) ^ (x̄11 _ x̄44 _ x̄51) · · ·
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big data analysis unsupervised learning
34
AI
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
sequential decision theory
ML Quantum linear algebra
Shallow quantum circuits
Adiabatic QC/ Quantum optimization
Quantum oracle identification
Quantum walks
supervised learning
Towards good-old-fashioned-AIQuantum solutions for combinatorial optimization
NB: NP not in BQP
-annealers-quantum-enhanced classical algorithms
even on small QCs
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35
classical
quantum
NP problems on smaller quantum computers
VD, Ge, Cirac, Phys. Rev. Lett. 121, 250501 (2018)
Works because structure is loose
For heuristic solutions… noise may not be a terminal problem
AI as the killer ap?
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big data analysis unsupervised learning
AI
online learning
generative models
reinforcement learning
deep learning
statistical learning
non-parametric learning
parametric learning
local search
Symbolic AI
computational learning theorycontrol theory non-convex
optimization
sequential decision theory
ML Quantum linear algebra
Shallow quantum circuits
Adiabatic QC/ Quantum optimization
Quantum oracle identification
Quantum walks
supervised learning
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Editor-in-ChiefGiovanniAcampora,UniversityofNaplesFedericoII,Italy
FieldEditors1)QuantumMachineLearningSethLloyd(MIT),USA2)QuantumComputing forArtificialIntelligenceHansJürgenBriegel,(Innsbruck, Austria)3)ArtificialIntelligenceforQuantum InformationProcessingChin-Teng Lin(Sydney,Australia)4)Quantum- andBio-inspiredComputational IntelligenceFranciscoHerrera(Granada,Spain)5)QuantumOptimizationDavide Venturelli (USRA,USA)
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