D-WaveQuantum ComputingAccess & applications via cloud deployment

Dr. Colin P. Williams
Vice President of Strategy & Corporate Development
D-Wave Systems Inc.
D-Wave Quantum Computing
Access & applications via cloud deployment

2Copyright © D-Wave Systems Inc.
D-Wave’s Mission & Activities
• Mission
– To solve the world’s hardest problems especially in the
areas of artificial intelligence and machine learning
• Core technologies
– Superconducting annealing-based quantum computers
– Hybrid quantum/classical algorithms & architectures
• Business model
– Quantum computer system sales
– Quantum computer cloud services
– Quantum machine learning services

What are Quantum
Computers?

What are Quantum Computers?
Computers that harness
quantum physical effects
not available to
conventional computers
Quantum
Processor

Superposition
Entanglement
Quantum Tunneling
Which Quantum Effects are Used?

Our Approach in Context
• Annealing (D-Wave, Google, IARPA)
– Harnesses Nature’s ability to find low energy configurations via quantum tunneling
– Resilient to noise / does not require long coherence times / MIT pedigree
– Handles a wide range of important problems
– Currently non-universal but could be made universal
• Gate Model (Google, IBM, Intel, Alibaba, Rigetti)
– Most common approach / based on analogy with Boolean logic circuits
– Very difficult to scale; requires massive qubit overhead for error correction
• Topological (Microsoft)
– Like gate model but without need for error correction (in theory)
– Needs exotic quasi-particle whose robustness is now in dispute
(Phys. Rev. Lett., 118, 046801, 26 Jan 2017)

D-Wave’s
Quantum Computer

Current Product: D-Wave 2000QTM

World’s Most Advanced Quantum Processor

Superconducting yet made in a CMOS Foundry
$1B World Class Production Facility 2000-qubit Circuits at 129,000 JJs .25μm design rules ASML 193nm lithography 65nm

Functional Quantum Computation Established
• Papers show superposition, entanglement & co-tunneling
– Johnson et al., “Q. Annealing with Manufactured Spins,” Nature 473, 194-198, 12th May (2011).
– T. Lanting et al., “Cotunneling in pairs of coupled flux qubits,” Phys. Rev. B 82, 060512(R) (2010).
– T. Lanting et al., “Entanglement in a Q. Annealing Processor,” Phys. Rev. X 4, 021041 (2014).
• These quantum effects play a functional role in the computations
– Boixo, et al., "Computational multiqubit tunneling in programmable quantum annealers," Nature Communications 7,
Article number: 10327, Published 07 January (2016).
• UCL/USC showed that none of the classical models so far proposed as
explanations for the D-Wave machine are correct
– Albash et al., “Consistency Tests of Classical and Quantum Models for a Quantum Annealer,” Phys. Rev. A 91, 042314,
Published 13 April (2015).
• USC & D-Wave showed q. annealing can occur successfully on timescales orders
of magnitude longer than the coherence time
– Albash et al., "Decoherence in adiabatic quantum computation," Phys. Rev. A 91, 062320 (2015).
– N G Dickson et al. “Thermally assisted quantum annealing of a 16-qubit problem”, Nature Communications 4, Article
number: 1903, 21 May (2013).

Is Quantum Computing Ready for Deployment?
http://www.fz-juelich.de/ias/jsc/EN/Research/ModellingSimulation/QIP/QTRL/_node.html
Jülich
Supercomputing
Center created a
framework for
Quantum Technology
Readiness Levels
D-Wave
quantum
annealer
IBM
Google
Experimental
qubit devices

The Potential

Potential for Massive Speedups
Copyright © 2017 D-Wave Systems Inc. 14
• Google found D-Wave 2X was 100,000,000x faster than QMC and
SA on a particular problem (their “quantumess” test)
• More competitive classical
algorithms become ineffective
as we move to higher
connectivity chips
See “What is the Computational Value of Finite Range Tunneling?” arXiv:1512.02206v3
• Apparent parallel scaling of
QMC & D-Wave is an artifact
(see E. Andriyash et al. “Can QMC simulate QA?”
arXiv:1703.09277)

Potential for Better Performance vs. Power Scaling
Source: http://www.extremetech.com/computing/116561-the-death-of-cpu-scaling-from-one-core-to-many-and-why-were-still-stuck
Quantum Power, ~0.1 μW
Classical Power
Classical
Performance
Quantum Performance
See: http://www.dwavesys.com/sites/default/files/14-1005A_D_wp_Computational_Power_Consumption_and_Speedup.pdf
• Transistors (000s)
• Clock Speed (MHz)
• Power (W)
• Perf/Clock (ILP)
Rainier
Vesuvius
Washington

Potential for Faster & Better (Lower Energy) SamplingEnergiesofSamplesReturned
Quantum Classical
Fat Tree #1
Classical
Fat Tree #2
Classical
Selby
Classical
SA #1
Classical
SA #2
Best sample so far

Quantum Sampling Accelerates Learning
• Specify model parameters θtrue, draw
exact Boltzmann samples from θtrue, and
estimate θ from samples
• Compare efficacy of CD, PCD, and QA-
seeded MCMC chains at estimating the
true distribution
• Compare rate of learning of a fully visible
probabilistic graphical model classically vs.
quantumly
Goal Model to Learn
Procedure
Classical
Learning
via PCD
Classical
Learning
via CD
Quantum Learning (learns true θ faster)
D. Korenkevych et al., “Benchmarking Quantum Hardware for Training of Fully Visible Boltzmann Machines,” arXiv:1611.04528
Result: Quantum Learns Faster

Factoring
Finding
Ramsey
Numbers
Diagnosis
Constraint
Satisfaction
Monte
Carlo
Financial
Modeling
SAT Filters
Discrete
Sampling
Complexity
Scaling
Quantum Error
Correcting Codes
Quantum
Simulation
Quantum
Research
Discrete
Optimization
Radiotherapy
Optimization
Deep Learning
Variational
Autoencoders
Boltzmann
Machines
Applications Customers Have Mapped to D-Wave
Optimization Sampling Science
Structured
Prediction
Trading
Trajectory
Optimization
Detecting
Market
Instability

Lowest Level Programming
Computational Problem to Solve
Equivalent Ising Problem
Run Quantum Annealing
Read Out a Spin-configuration having
Low Energy
Embedded Ising Problem
Retain all Solutions
(SAMPLING)
Retain Best Solution
(OPTIMIZATION)
Store Spin
Configuration & Repeat

Programming Languages & Software Tools
• Programming Languages
– Python, Matlab, C/C++
• Compilers
– Map problem to Ising problem
• Embedders
– Ising problem to processor graph
• Pre-processing
– Determining any forced variables
– Decomposing larger problems
• Post-processing (optional)
– Seeding heuristic optimizers
– Inline GPU & CPU computations

Applications
in Finance

PROBLEM: Invest $K amongst N assets at T time steps so as to
maximize expected returns subject to varying risk
and transaction costs at each time step
APPROACH: Quantum Optimization via D-Wave
• Couch problem as a quadratic integer optimization
problem
• Map integer constraints to QUBOs
• Minimize sum of QUBOs via quantum annealing
Returns
at each
time step
Transaction Costs
Sum of holdings at each time step = K
Max allowed holding of each asset = K’
Risk:
Σ = forecast
covariance matrix;
γ = risk aversion
Optimization: Solving the OptimalTradingTrajectory Problem
Using a Quantum Annealer arXiv1508.06182
IMPACT:
Finds optimal
strategy subject
to realistic
constraints
G. Roseberg et al (1QBit), M. L. de Prado (Guggenheim Partners), P. Carr (Courant Inst.) & K. Wu (LBL)

PROBLEM: Seek signature of impending market instability by detecting onset of
anomalously correlated moves
APPROACH: Model market as a graph; nodes = assets; edge if correlation > c
• Continually re-compute largest clique / Sudden expansion in clique size signals market move
Optimization: Impending Market Instability
IMPACT: Signals imminent market instability

Application in
Healthcare

• Represent a model as a bit string
• HPC: bit string -> model -> simulation -> evaluation -> “score”
• D-Wave: Learn from results, adjust the program QC runs & iterate
• So QC guesses solution / HPC scores it / Adjust QC & repeat
Quantum-Accelerated Optimization
Better “guesses”
“Scores” for the guesses
Use QC to reduce number of calls to HPC

Why Does it Work?
• Imagine you’ve reached an intermediate point in design space and
want to pick the next bit string to try
• Classical methods only sense the local neighborhood
• Quantum methods have potential for greater horizon
• Make a better next move possibly leading in different direction
Classical
Discrepancy
Design Parameter
Quantum
Discrepancy
Design Parameter

Case Study: Radiotherapy Optimization
PROBLEM: Deliver lethal dose to tumor whilst minimizing
damage to healthy tissues
APPROACH: Hybrid: QC + Conventional Computer
• Radiation treatment plan = bit string
• Quality = result of running extensive
radiation transport simulation
• Results of radiation transport simulations
drive adjustments to plan
IMPACT:
• Hybrid quantum-classical design found a radiation therapy
treatment that minimized the objective function to 70.7 c.f. 120.0
for tabu, and ran in 1/3 the time making fewer calls to radiation
transport sim. Source: “Varian’s RapidArc Radiation Delivery
System Goes Clinical,” medGadget, July 22nd (2008)

Applications in
Machine Learning

People Have Used D-Wave for Machine Learning
• Mainly supervised learning so far
– Yes/No classifier for cars in images
– Wink/Blink classifier
– Yes/No Higgs boson event classifier
Source: A. Mott, J. Job, J. Vlimant, D. Lidar & M. Spiropulu, Nature, Volume 550, 19th October 2017.

What Current A.I. Doesn’t Do Well
“Unsupervised learning had a catalytic effect in reviving interest in
deep learning, but has since been overshadowed by the successes of
purely supervised learning. […] we expect unsupervised learning to
become far more important in the longer term. Human and animal
learning is largely unsupervised: we discover the structure of the
world by observing it, not by being told the name of every object.”
Yann LeCun, Yoshua Bengio & Geoffrey Hinton,
“Deep Learning,” Nature, Vol. 521, 28th May (2015)
• A.I. is not yet sufficiently good at unsupervised learning

Quantum Computers Can Help
• Unsupervised learning can use probabilistic models
• These rely on sampling
• Quantum computers have potential to revolutionize A.I. by making
unsupervised learning models feasible to train efficiently
• Because quantum computers are fast native samplers

How does Sampling Arise in Probabilistic Models?
• Consider a Restricted Boltzmann Machine (RBM)
• RBMs can be components of more complex neural networks
Model parameters q º {bi}È{cj}È{Wi j}
Visible units with biases bi
Hidden units with biases cj
W1,1
W1,2
W10,10

What does Training Entail? Discrete Sampling!
• Given training data (visible vectors) vt s.t. 1 ≤ t ≤ T
• Adjust model parameters s.t. model most likely reproduces the training data
• Done by maximizing the log-likelihood of the observed data distribution w.r.t.
the model parameters, θi
¶
¶qi
log(p(vt ))
t=1
T
å
æ
è
ç
ç
ö
ø
÷
÷ = -
¶
¶qi
E(vt,h)
t=1
T
å
p(h |v
t
)
+T
¶
¶qi
E(v,h)
p(v, h)
• Positive Phase
• Expectation over p(h|vt)
in “clamped” condition
• Requires sampling over the
(given) data distribution
• Simple!
• Negative Phase
• Expectation over p(v, h) in
“unclamped” condition
• Requires sampling over the
(predicted) model distribution
• Intractable!
where

ooooDirected hierarchical
aanetwork of continuous
variables
Directed hierarchical
aanetwork of continuous
oooovariables
Discrete Sampling in Complex Architectures (DVAE/QVAE)
• Real data has discrete & continuous variables
• Natural to want discrete hidden variables
• Can’t backpropagate through discrete
variables
• DVAE solves this problem
– See J. Rolfe, “Discrete Variational Autoencoders”,
arXiv:1609.02200 Undirected network of discrete variables
(a fully hidden bipartite (possibly quantum)
Boltzmann machine
Encoder Network
Decoder Network
Sample from smoothed distribution
Smoothed (i.e., continuous) discrete
latent variables
Random samples
from U[0,1]
• Exceeds state of the art on three standard
machine learning datasets
• DVAE (classical) / QVAE (quantum)

Training Digits
DVAE
Previous State
of the Art
J. Rolfe, “Discrete Variational Autoencoders”, arXiv:1609.02200 [stat.ML]
DVAE Exceeds State-of-the-Art on a Generative Task
Machine-Generated Novel DigitsReconstructed Digits

Why we Believe QVAE will Further Improve DVAE
State-of-the-Art (classical) DVAE (classical) QVAE (via QMC simulation)
Same number of training epochs used in each case

Quantum/Classical Machine Learning Services
• D-Wave web services are designed to
make it easier to train PML models
• Capabilities
– Learns from noisy / incomplete data
– Quantifies confidence in predictions
– Reveals hidden correlations in data
– Infers missing data
• Functionality (Web Services for PML):
– Classical Boltzmann sampling (GPU)
– Quantum Boltzmann sampling
(CPU)
– Raw QPU sampling (QPU)
• Supports both ML/QML models
• Called from TensorFlow or Python

Hybrid
Quantum/Classical
Cloud Model

Quantum Cloud
• Quantum computers …
– Need typical datacenter infrastructure
– Are expensive
– Are evolving fast / quickly obsolete
– Are alien to most programmers
• Solution
– Make QCs accessible via the cloud
– Bill usage by minute or by time blocks
– Lease QC time rather than buy QC
– Access via familiar software & tools
– Includes classical proxy solvers for code
development & debugging

Bill Gates Expects Quantum Cloud Access [by 2026]
Source: http://www.zdnet.com/article/quantum-cloud-computing-could-arrive-in-the-next-decade-says-bill-gates/

D-Wave Sells Quantum Cloud Access Already
Jane Edwards, "D-Wave to Provide Oak Ridge National Lab Cloud Access to Quantum Computing", ExecutiveBiz.com blog post, July 26th, (2017) web URL
http://blog.executivebiz.com/2017/07/d-wave-to-provide-oak-ridge-national-lab-cloud-access-to-quantum-computing-platform/

Conclusions
• Quantum computing will turbo-charge unsupervised learning
• Quantum and hybrid machine learning models already running
• Our first web-ML services were released in September 2017
– Reinvigorate probabilistic machine learning and prepare ground for
future quantum & hybrid ML services
– Both state-of-the-art today (classically) / faster tomorrow (quantumly)
• DVAE already surpassing state of the art / QVAE coming in 2018
• Seeking users for our quantum cloud services!
Contact: cpwilliams@dwavesys.com

Thank you!
Email: cpwilliams@dwavesys.com

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