An Introduction to Quantum Computing, Probably

Washington Seminars

Bo Ewald October 17, 2017

Bo Ewald April 4-5, 2018

Company Confidential TOPICS

•Introduction to Quantum Computing •D-Wave Quantum Systems •Early Applications •2018 & Beyond •Questions

1960 1970 1980 1990 2000 2010 2020

Title: Los Alamos Experience Author: Phyllis K Fisher Page 247

• Exploits quantum mechanical effects • Built with “qubits” rather than “bits” • Operates in an extreme environment • Enables quantum algorithms to solve very hard problems

Quantum Processor

Binary

Separable

Barriers

Superposition

Entanglement

Quantum Tunneling

Quantum key distribution

Quantum information processing

Quantum Quantum Annealing Topological Quantum Sensor Computing

Quantum Gate Model Emerging Communication

Quantum Cryptography Topological Ion Trap

Preparation Rotation by Readout of singlet state �1 and �2 measurement

IBM QX, Yorktown Heights, USA

X X-gate: U1 phase-gate: Xȁ0ۧ = ȁ1ۧ U1ȁ0ۧ = ȁ0ۧ, U1ȁ1ۧ = ��ȁ1ۧ Xȁ1ۧ = ȁ0ۧ CNOT gate: C01ȁ0100ۧ = ȁ0100ۧ Hadamard gate: H C01ȁ0110ۧ = ȁ1110ۧ Hȁ0ۧ = ȁ0ۧ + ȁ1ۧ / 2 C01ȁ1100ۧ = ȁ1100ۧ + Hȁ1ۧ = ȁ0ۧ − ȁ1ۧ / 2 C01ȁ1110ۧ = ȁ0110ۧ

10 “Computing with Quantum Knots”*

*Graham P. Collins Scientific American 294 2006 pp. 56-63

•Introduction to Quantum Computing •D-Wave Quantum Systems •Early Applications •2018 and Beyond •Questions

1950 1960 1970 1980 1990 2000 2010

PHYSICAL REVIEW E VOLUME 58, NUMBER 5 NOVEMBER 1998

Quantum annealing in the transverse Ising model Tadashi Kadowaki and Hidetoshi Nishimori Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152- 8551, Japan (Received 30 April 1998)

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach. The idea is tested by the transverse Ising model, in which the transverse field is a function of time similar to the temperature in the conventional method. The goal is to find the ground state of the diagonal part of the Hamiltonian with high accuracy as quickly as possible. We have solved the time-dependent Schrödinger equation numerically for small size systems with various exchange interactions. Comparison with the results of the corresponding classical (thermal) method reveals that the quantum annealing leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule. [S1063-651X~98!02910-9]

1960 1970 1980 1990 2000 2010 2020

• Founded in 1999 • World’s first quantum computing company • Public customers: – Lockheed Martin/USC – Google/NASA Ames/USRA – Los Alamos National Laboratory – Cybersecurity - 1 – Oak Ridge National Laboratory • Other customer projects done via cloud access • ~150 U.S. patents

Copyright © D-Wave Systems Inc. 18 But, It Is Fundamentally Different Than Anything You’ve Ever Done Before! Intel 64 D-Wave Performance (GFLOPS) ~20 (12 cores) 0 Precision (bits) 64 4-5 MIPS ~12,000 (12 cores) 0.01

Instructions 245+ (A-M) 251+ (N-Z) 1

Operating Temp. 67.9° C -273° C Power Cons. 100 w +/- ~0

Devices 4B+ transistors 2000 qubits

Maturity 1945-2016 ~1950’s

• 16 Layers between the quantum chip and the outside world

• Shielding preserves the quantum calculation

• Cooled to 0.015 Kelvin, 175x colder than interstellar space • Shielded to 50,000× less than Earth’s magnetic field • In a high vacuum: pressure is 10 billion times lower than atmospheric pressure

• On low vibration floor 15mK • <25 kW total power consumption – for the next few generations

10,000

1,000

Number of 100 Qubits

•Introduction to Quantum Computing •D-Wave Quantum Systems •Early Applications •2018 and Beyond •Questions

• Optimization

• Machine Learning

• Monte Carlo/Sampling

• Material Science

• Lockheed/USC ISI • Los Alamos National Laboratory – Software Verification and – Optimization Validation – Machine Learning, Sampling – Optimization – Aeronautics – Software Stack – Performance Characterization & – Simulating Quantum Systems Physics – Other (good) Ideas • Google/NASA Ames/USRA • CS - 1 – Machine Learning – Cybersecurity – Optimization • Oak Ridge National Laboratory – Performance Characterization & Physics – Similar to Los Alamos – Research – Material Science & Chemistry

Round 1 (June 2016) Round 2 (December 2016) 1. Preprocessing Methods for Scalable Quantum Annealing 1. Accelerating Deep Learning with Quantum Annealing 2. QA Approaches to Graph Partitioning for Electronic Structure Problems 2. Constrained Shortest Path Estimation 3. Combinatorial Blind Source Separation Using “Ising” 3. D-Wave Quantum Computer as an 4. Rigorous Comparison of “Ising” to Established B-QP Efficient Classical Sampler Solution Methods 4. Efficient Combinatorial Optimization using Quantum Computing Round 3 (January 2017) 5. Functional Topological Particle Padding 1. The Cost of Embedding 6. gms2q—Translation of B-QCQP to 2. Beyond Pairwise Ising Models in D-Wave: Searching for D-Wave Hidden Multi-Body Interactions 7. Graph Partitioning using the D-Wave for 3. Leveraging “Ising” for Random Number Generation Electronic Structure Problems 4. Quantum Interaction of Few Particle Systems Mediated 8. Ising Simulations on the D-Wave QPU by Photons 9. Inferring Sparse Representations for 5. Simulations of Non-local-Spin Interaction in Atomic Object Classification using the Magnetometers on “Ising” Quantum D-Wave 2X machine 6. Connecting “Ising” to Bayesian Inference Image Analysis 10. Quantum Uncertainty Quantification for 7. Characterizing Structural Uncertainty in Models of Physical Models using ToQ.jl Complex Systems 11. Phylogenetics calculations 8. Using “Ising” to Explore the Formation of Global Terrorist Networks

Los Alamos National Laboratory

Use Case 2016 2017 Total % Combinatorial Optimization 5 5 10 45% Machine Learning, Sampling 2 2 4 18% Understanding Device Physics 2 1 3 14% Software Stack/Embeddings 1 1 2 9% Simulating Quantum Systems 2 2 9% Other (good) Ideas 1 1 5% Total 11 11 22 100%

The LANL Rapid Response Project results for 2016 and 2017 are available as PDF’s at: http://www.lanl.gov/projects/national-security-education-center/information-science- technology/dwave/index.php

Los Alamos National Laboratory 6/27/2017 ISTI Rapid Response DWave Project (Dan O’Malley): Nonnegative/Binary Matrix Factorization

▪ Low-rank matrix factorization

• � ≈ �� where ��,� ≥ 0 and ��,� ∈ {0,1} (1999)

• � ≈ � � Nature , ▪ Unsupervised machine-learning application • Learn to represent a face as a linear combination of basis images Image credit: Lee & Seung • Goal is for basis images to correspond to intuitive notions of parts of faces ▪ “Alternating least squares” 1. Randomly generate a binary �

2. Solve � = arg min� ∥ � − �� ∥� classically

3. Solve � = arg min� ∥ � − �� ∥� on the D-Wave 4. Repeat from step 2 ▪ Results • The D-Wave NMF approach results in a sparser � (85% vs. 13%) and denser but more lossy compression than the classical NMF approach • The D-Wave outperforms two state-of-the-art classical codes in a cumulative time-to-target benchmark when a low-to-moderate number of samples are used

UNCLASSIFIED Nov. 13, 2017 | 30 ISTI Rapid Response DWave Project (Hristo Djidev): Efficient Combinatorial Optimization

▪ Objectives • Running on larger (Chimera-like) graphs • Develop D-Wave (DW) algorithms for NP-hard o Chimera graph is problems modified by merging a set of randomly Focus: the max clique (MC) problem: selected edges into a vertex o Resulting graphs of sizes upto 1000 are used as inputs

probSedges:S3068,SEnergySprobSupperSbound:S3930.5

orig.graph cliqueofmaxsize to MC problem -2 2 Vertices -1 1 Couplers

SolutionS: -1 +1 • Study scalability/accuracy issues and ways to o DW beats simulated mitigate them annealing, its classical analogue, by a • Characterize problem instances for which D- factor of more than 106 Wave may outperform classical alternatives Quality comparison Speed comparison ▪ Results • The MC problem can be solved accurately and fast on DW o but so can classical methods o no quantum advantage for typical problem instances fitting DW (of size ~45) o In order to see a quantum advantage for the MC problem, graph sizes should be > 300 UNCLASSIFIED Nov. 13, 2017 | 31 ISTI Rapid Response DWave Project (Sue Mniszewski): Quantum Annealing Approaches to Graph Partitioning for Electronic Structure Problems

▪ Motivated by graph-based methods for

quantum molecular dynamics (QMD) k-Concurrent Partitioning for simulations Phenyl Dendrimer. ▪ Explored graph partitioning/clustering methods formulated as QUBOs on D-Wave 2X

▪ Used sapi and hybrid classical-quantum k-parts METIS qbsolv qbsolv software tools 2 705 706

▪ Comparison with state-of-the-art tools 4 20876 2648

▪ High-quality results on benchmark (Walshaw), 8 22371 15922 random, and electronic structure graphs 16 28666 26003 Graph N Best METIS KaHIP qbsolv k-Concurrent clustering for Add20 2395 596 723 613 602 IGPS Protein Structure: 3elt 4720 90 91 90 90 resulting 4 communities share common sub- Bcsstk33 8738 10171 10244 10171 10171 structure. Comparable to classical methods. Minimize edge counts between 2 parts on Walshaw graphs.

UNCLASSIFIED Nov. 13, 2017 | 32 ISTI Rapid Response Project (Carleton Coffrin): Challenges and Successes of Solving Binary Quadratic Programming Benchmarks on the DW2X QPU

▪ Looking to the Future • I have drunk D-Wave Kool-Aid • RAN1 convinced me that the DW2X has huge potential • I believe, in the next 5 years, QPU’s will be very disruptive to optimization research

UNCLASSIFIED Nov. 13, 2017 | 33 Quantum Computing for NASA Applications

Objective: Find “better” solution • Faster • More precise • Not found by classical algorithm

Anomaly Data Analysis Detection and and Data Fusion Decision Making

V&V and Air Traffic Optimal Management Sensor Placement

Topologically- aware Parallel Computing Mission Planning, Scheduling, and Coordination

Common Feature: Intractable problems on classical supercomputers

Biswas, SMC-IT, 28 Sept 2017 34 Current NASA Research in Annealing Applications Complex Planning and Scheduling • General Planning Problems (e.g., navigation, scheduling, asset allocation) can be solved on a quantum annealer (such as D-Wave) • Developed a quantum solver for Job Shop Scheduling that pre-characterizes instance ensembles to design optimal embedding and run strategy – tested at small scale (6x6) but Graph-based Fault Detection potentially could solve intractable problems Circuit 15 (15x15) with 10x more qubits 17 16 19 Breakers 14 31 46 33 44 21 4 32 30 35 • Analyzed simple graphs of Electrical Power 13 45 37 5 29 20 36 1 11 27 34 Networks to find the most probable cause of 3 41 42 18 26 39 40 10 28 24 43 2 Sensors 22 8 38 multiple faults – easy and scalable QUBO 25 12 23

6 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 Observations 9 mapping, but good parameter setting (e.g., 7 gauge selection) key to finding optimal solution – Machine Learning now exploring digital circuit Fault Diagnostics • Boltzmann sampling commonly used in IN: OUT: Machine Learning, particularly Deep Learning. configs. params. Quantum computing has provable advantage for QA {J , h} some sampling problems. Demonstrated learning when using a QA as a Boltzmann sampler. Scheduling Applications Planner Comparison: All Scheduling Problems

10,000 FF:a=1.11 ± 0.061 LPG: a=0.69 ± 0.139 1000 M: a=0.1 ± 0.007 ]

c Mp: a=0.54 ± 0.035

Comparison with e s [ 100 e m i state-of-the-art t n

u 10 R

n a application-specific i 1 d e algorithms: M Graph coloring 0.1 current best planners 0.01

10 20 30 40 50

Problem size n: number of tasks Eleanor G. Rieffel, Davide Venturelli, Minh Do, Itay Hen, Jeremy Frank, Parametrized Families of Hard Planning Problems from Phase Transitions, AAAI-14. D-Wave run results: established baseline E. G. Rieffel, D. Venturelli, B. O'Gorman, M. B. Do, E. Prystay, V.N. Smelyanskiy, A case study in programming a quantum annealer for hard performance for QA on these applications operational planning problems, Q. Information Processing, 14, (2014)

Solved problems with 6 machines and 6 jobs: QA-guided tree search analyzed scaling of tractability Job-Shop scheduling: Complete quantum- Mars Lander activity classical solver framework with pre- scheduling processing, compilation/run strategies, Airport decomposition methods runway scheduling D. Venturelli, D. J.J. Marchand, G. Rojo, Quantum Annealing Implementation of Job Shop Scheduling, arXiv:1506.08479 • T. Tran, M. Do, E. Rieffel, J. Frank, Z. Wang, B. O'Gorman, D. Venturelli, J. Beck, A Hybrid Quantum-Classical Approach to Solving Scheduling Problems, SOCS’16 Scheduling problems as testbed for resource- • T. Tran, Z. Wang, M. Do, E. Rieffel, J. Frank, B. O'Gorman, D. Venturelli, J. Beck, Explorations of Quantum-Classical Approaches to Scheduling a Mars Lander bounded tailored embedding methods Activity Problem, Workshops AAAI’16 Fault Diagnosis

First comprehensive study addressing the readiness of quantum annealing for real-world applications Six different algorithms (SA, PT-ICM, QMC, SAFARI, SAT-based, and DWave2X) In all three problem Hamiltonian representations (PUBO, QUBO, Chimera) Addressed future quantum annealer design for quantum advantage in applications with practical relevance • What is the impact of higher-order terms? • Need for non-stoquastic Hamiltonians? • Impact of connectivity? …

A. Perdomo-Ortiz et al., On the readiness of quantum optimization machines for industrial applications arXiv:1708.09780 A near-term approach for quantum-enhanced machine learning

• Hybrid proposal that works directly on a low-dimensional representation of the data. New paradigm: Use deep learning to assist QML implementation in near-term QC

Quantum sampling Quantum Quantum processing

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

Raw input data Training Generated

Classical pre Classical samples samples

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). Newly funded effort in aeronautics Feasibility study: Using quantum-classical hybrids to assure the availability of the UAS Traffic Management (UTM) network against communication disruptions Future • Higher vehicle density • Heterogeneous air vehicles • Mixed equipage • Greater autonomy • More vulnerability to communications disruptions Explore quantum approaches to Kopardekar, P., Rios, J., et. al., Unmanned Aircraft System Traffic • Robust network design Management (UTM) Concept of Operations, DASC 2016 • Track and locate of a moving jammer 30 month effort: harness the power of quantum • Secure communication of codes computing and communication to address the supporting anti-jamming protocols cybersecurity challenge of availability Joint with NASA Glenn, who are working Prior work (NASA-DLR collaboration): T. Stollenwerk et al., on QKD for spread spectrum codes Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management Mission To help solve the most challenging problems in the multiverse:

• Optimization

• Machine Learning

• Monte Carlo/Sampling

• Material Science

D-Wave Users Group Meeting - National Harbour, MD 27.09.2017 – Dr. Gabriele Compostella The Question that drove us …

Is there a real-world problem that could be addressed with a Quantum Computer?

27.09.2017 K-SI/LD | Dr. Gabriele Compostella 42 YES: Traffic flow optimisation

Everybody knows traffic (jam) and normally nobody likes it. Image courtesy of think4photop at FreeDigitalPhotos.net

27.09.2017 K-SI/LD | Dr. Gabriele Compostella 43 Public data set: T-Drive trajectory https://www.microsoft.com/en-us/research/publication/t-drive-trajectory-data-sample/

Beijing • ~ 10.000 Taxis • 2.2. – 8.2.2008

data example:

27.09.2017 K-SI/LD | Dr. Gabriele Compostella 44 Result: unoptimised vs optimised traffic

27.09.2017 K-SI/LD | Dr. Gabriele Compostella 45 Volkswagen Quantum Computing in the news

27.09.2017 K-SI/LD | Dr. Gabriele Compostella 46 27.09.2017 K-SI/LD | Dr. Gabriele Compostella 47 HETEROGENEOUS QUANTUM COMPUTING FOR SATELLITE OPTIMIZATION

GID E ON B AS S BOOZ AL L EN HAMILTON

September 2017 Combinatorial Chemistry

QUANTUM Vehicle Machine ANNEALING HAS Routing Learning

MANY REAL- Traveling Drug Artificial Discovery WORLD Salesman Intelligence APPLICATIONS Circuit Design Manufacturing

Network Logistics Design Robotics

Booz Allen Hamilton Restricted, Client Proprietary, and Business Confidential.

BOO Z ALLEN • DIG IT A L System Optimization Design + As problems and datasets grow, modern computing systems have had to scale with them. Quantum computing offers a totally new and potentially disruptive computing paradigm. CONCLUSIONS + For problems like this satellite optimization problem, heterogeneous quantum techniques will be required to solve the problem at larger scales.

+ Preliminary results on this problem using heterogeneous classical/quantum solutions are very promising.

+ Exploratory studies in this area have the potential to break new ground as one of the first applications of quantum computing to a real-world problem

Booz Allen Hamilton Restricted, Client Proprietary, and Business Confidential.

BOO Z ALLEN • DIG IT A L 18 Display Advertising Optimization by Quantum Annealing Processor

Shinichi Takayanagi*, Kotaro Tanahashi*, Shu Tanaka† *Recruit Communications Co., Ltd. † Waseda University, JST PRESTO Behind the Scenes

SSP DSP Publisher Advertiser Winner! AD 1.0$

Impression RTB AD 0.9$ SSP: Supply-Side Platform 0.7$ DSP: Demand-Side Platform RTB: Real Time Bidding 52

（C）Recruit Communications Co., Ltd. CTR Prediction with Machine-Learning

(Click-through-rate) • Machine-Learning (ML) tech is often used for CTR prediction • ML has succeeded in this field Users Matrix expression Click or Not Click F1 F2 F3 Prediction

1 M 01 2.13 Model 0 F 07 2.12 0 F 23 4.2 ? F 99 1.2

53 （C）Recruit Communications Co., Ltd. Budget Pacing

Target budget • Budget pacing is also important 16 Too fast • Control of budget pacing helps 12 advertisers to… – Reach a wider range of audience 8

– Avoid a premature campaign spending Budget 4 Budget pacing controlled stop / overspending 0 0 6 12 18 Time (hours)

54 （C）Recruit Communications Co., Ltd. 4. Summary

• Budget pacing is important for display advertising • Formulate the problem as QUBO • Use D-Wave 2X to solve budget pacing control optimization problem • Quantum annealing finds a better solution than the greedy method.

55 （C）Recruit Communications Co., Ltd. DENSO Optimization Projects

Videos from CES, Las Vegas, January 2018

Autonomous Driving https://www.youtube.com/watch?v=Bx9GLH_GklA

Factory Optimization https://www.youtube.com/watch?v=BkowVxTn6EU

• Optimization

• Machine Learning

• Monte Carlo/Sampling

• Material Science

Copyright © D-Wave Systems Inc. 57 ORNL is managed by UT-Battelle for the US Department of Energy 58 billings7893 A Study of Complex Deep Learning Networks on High Performance, Neuromorphic, and Quantum Computers

There are currently 3 main challenges in Deep Learning

The First:

Adiabatic Quantum Programming at ORNL: Workflow Environments and HPC Integration APIs

59 Presentation_name Quantum Machine Learning for Election Modelling Election 2016: Case study in the difficultly of sampling

Where did the models go wrong?

Quantum Machine Learning for Election Modelling – Max Henderson, 2017 6 1 Forecasting elections on a quantum computer

• Quantum computing research has shown potential benefits (speedups) in training various deep neural networks1-3

• Core idea: Use QC-trained models to simulate election results. Potential benefits: • More efficient sampling / training • Intrinsic, tuneable state correlations • Inclusion of additional error models

1. Adachi, Steven H., and Maxwell P. Henderson. "Application of quantum annealing to training of deep neural networks." arXiv preprint arXiv:1510.06356 (2015). 2. Benedetti, Marcello, et al. "Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning." Physical Review A 94.2 (2016): 022308. 3. Benedetti, Marcello, et al. "Quantum-assisted learning of graphical models with arbitrary pairwise connectivity." arXiv preprint arXiv:1609.02542 (2016).

Quantum Machine Learning for Election Modelling – Max Henderson, 2017 6 2 Summary

• The QC-trained networks were able to learn structure in polling data to make election forecasts in line with the models of 538 • Additionally, the QC-trained networks gave Trump a much higher likelihood of victory overall, even though the state’s first order moments remained unchanged • Ideally in the future, we could rerun this method using correlations known with more detail in-house for 538 • Finally, the QC-trained networks trained quickly, and since each measurement is a simulation, each iteration of the training model produced 25,000 simulations (one for each national error model), which already eclipses the 20,000 simulations 538 performs each time they rerun their models

Quantum Machine Learning for Election Modelling – Max Henderson, 2017 63 Quantum Enabled Machine Learning

Supervised Learning: Improving Neural Network Training 1 2 3 4 5 6 7 8

e e e e e e e e d d d d d d d d o o o o o o o o n n n n n n n n

e e e e e e e e l l l l l l l l b b b b b b b b i i i i i i i i

visible hidden s s s s s s s s i i i i i i i i layer layer v v v v v v v v

hidden node 1

hidden node 2

hidden node 3

hidden node 4

hidden node 5

hidden node 6

hidden node 7

hidden node 8

Adachi, Steven H., and Maxwell P. Henderson. "Application of Quantum Annealing to Training of Deep Neural Networks." arXiv preprint arXiv:1510.06356 (2015).

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 Los Alamos National Laboratory

28-Sep-2016 | 66 Mission To help solve the most challenging problems in the multiverse:

• Optimization

• Machine Learning

• Monte Carlo/Sampling

• Material Science

R. Harris

3D transverse-field Ising model

A. King E. Dahl

Kosterlitz-Thouless model Z(2) lattice gauge theory

•Introduction to Quantum Computing •D-Wave Quantum Systems •Early Applications •2018 and Beyond •Questions

• ~50 – 100 qubit models running • No large scale error correction • Noisy Intermediate Scale QC’s (NISC)* • Know if some problems will run without error correction • Quantum Material Science? • No Shor’s Algorithm • Quantum “Supremacy” perhaps for synthetic benchmark • Importance of error correction and potential apps becomes clear * “Quantum Computing in the NISC era and beyond”, John Preskill, Cal Tech, arXiv:1801.00862

• 75 – 100 “proto-apps” on 2000Q D-Wave System • ~ Half approaching classical performance on smallish problems • Demonstrate Quantum Material Science breakthrough • Quantum “Advantage” demonstrations • IARPA QEO and D-Wave higher coherence 15mK qubit demonstrations • Trajectory to 4000-5000 qubit system, better connectivity, lower noise

• Big overseas investments in QC – China $11B – EU Flagship $1B – Japan Christmas Day meeting • U.S. and Canada – fragmented – 2019 U.S. budget proposal – DOE $100M, NSF $30M, others? • Quantum Diversity • More smart people working on apps and software tools

• Bo’s Unified Theory of Quantum Computing

Quantum Computing needs you to: Just Do It™ Probably

D-Wave Users Group Presentations: – https://dwavefederal.com/qubits-2016/ – https://dwavefederal.com/qubits-2017/

LANL Rapid Response Projects: – http://www.lanl.gov/projects//national-security-education- center/information-science-technology/dwave/index.php

Washington DC & Fort Meade Seminars April 4-5, 2018 Denny Dahl Quantum Material Science @ D-Wave

R. Harris

3D transverse-field Ising model

A. King E. Dahl

Kosterlitz-Thouless model Z(2) lattice gauge theory

Physical device that allows one qubit to influence another qubit COUPLER ��j

Real-valued constant associated with each qubit, which influences

WEIGHT �� the qubit’s tendency to collapse into its two possible final states; controlled by the programmer Real-valued constant associated with each coupler, which controls STRENGTH �� the influence exerted by one qubit on another; controlled by the programmer Real-valued function which is minimized during the annealing cycle OBJECTIVE ��

��(��, ��; ��) = ෍ �� + ෍ �� The system samples from the �� that minimize the objective

International Journal of Theoretical Physics, Vol. 21, Nos. 6/7, 1982

Quantum Hamiltonian is an operator on Hilbert space:

� � � � ℋ � = � � ෍ �� + � � ෍ �� + ෍ �� <�

transverse field

Corresponding classical optimization problem:

Obj(��, ��; ��) = ෍ �� + ෍ �� <�

Anneal Pause Anneal Quench Specify start and duration of Specify when to abruptly global pause in anneal quench transverse field

Anneal Offsets Reverse Anneal Per-qubit control over Begin and end the anneal in transverse field a classical state

Chimera topology is two dimensional!

Four red qubits are 2x2 grid of unit cells linked together to with eight qubits form a single logical apiece qubit; likewise for blue, aqua, green, …

anti-vortex

vortex

At high temperatures the vortices and anti-vortices interact weakly. At low temperatures the vortices and anti-vortices form bound pairs. The temperature at which the change occurs is the Kosterlitz-Thouless phase transition.

By varying parameters controlling the reverse annealing trajectory, King et al were able to measure order parameters which indicated that the system emulated the 2D XY model in both the paramagnetic phase (unbound vortex/anti-vortex) and the KT phase (bound vortex/anti-vortex).

Square-octagonal lattice

Gauge theories & groups: ➢ Elec & Magnetism: �(1) ➢ Weak force: ��(2)� ➢ Strong force: ��(3)

Gauge theories in 3+1 link variables � dimensional space-time have �� infinities and must be � � �� regularized. � plaquette � �� One approach is to replace space-time with a lattice. Example: 2D lattice, Z(2) gauge group

Physical problem: Embedded problem: 8x8 array of plaquettes 16x16 array of unit cells 9x8x2 = 144 spins 2048 qubits

GMQCs are designed to apply a sequence of gates – one at a time. If we are simulating a physical system in which many degrees of freedom are interacting simultaneously, perhaps this is an inefficient architecture.

• Annealing controls on the DW-2000Q provide more flexibility: ➢ Allows per qubit tuning to retard or advance annealing ➢ Anneal pause holds quantum Hamiltonian static ➢ Reverse annealling allows for Monte Carlo sampling • Quantum material simulation is now practical: ➢ 3D Transverse Field Ising Model ➢ KT transition in triangular and square-octagonal lattices ➢ Lattice gauge theory with finite gauge groups (work-in-progress) • Relevant for modeling: ➢ 3D magnetic materials and spin glasses ➢ Thin film and bulk topological insulators, superconductors and metals ➢ Lattice models with local symmetries

April 4, 2018 Max Henderson, Ph.D. QxBranch Overview

QxBranch delivers revolutionary data analytics software enabled by classical and emerging quantum computing capabilities that drive business value

Data Analytics | Quantum Computing | Systems Engineering Apply data analytics expertise and software capabilities to Established 2014 in Washington D.C. / London / Adelaide manage complex data and provide actionable insights across Team of ~20 software and systems engineers, data scientists multiple verticals Clients: Business domain expertise in finance, aerospace, defence, Global Investment Banks and technology domains Asset Management Firms Research & Development partnerships with clients and Technology Companies academia to identify business challenges that can be solved Government through cutting-edge applications of quantum computing Energy (universal and adiabatic) and advanced data analytics Pharmaceutical

QxBranch, Inc. 2018 2 Election 2016: Case study in the difficultly of sampling

Where did the models go wrong?

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 3 State-by-state correlations • Major issue: failure to model correlations1-3 between states • Most models assumed independence between results of each state • An accurate correlation matrix can capture higher- level, richer structure in the data and account for systemic errors in polls

1. http://www.independent.co.uk/news/world/americas/sam-wang-princeton-election-consortium-poll-hillary-clinton-donald-trump-victory-a7399671.html 2. http://elections.huffingtonpost.com/2016/forecast/president 3. http://money.cnn.com/2016/11/01/news/economy/hillary-clinton-win-forecast-moodys-analytics/index.html 4. http://fivethirtyeight.com/

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 4 Difficulty of sampling from correlated graphs • Even with perfect data on correlations between states, using the correlation matrix is difficult due to the computational cost of sampling from fully-connected graphs

• Sampling from fully-connected graphs is analogous to sampling from a properly trained Boltzmann machine • Training coefficients of Boltzmann machines requires performing calculations on all possible states of the model • As this is intractable on large problem sizes, heuristics or other models are typically implemented instead

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 5 Forecasting elections on a quantum computer • Quantum computing (QC) research has shown potential speedups in training deep neural networks1-3

• Core idea: By using QC-trained models to simulate election results we can achieve: • More efficient sampling / training • Intrinsic, tuneable state correlations • Inclusion of additional error models

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 6 What we ARE doing vs. what we AREN’T

Subject Matter Expertise Model(s) Simulation Model(s)

Data to Model

1. Individual state predictions

2. State Correlations

Simulation Results

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 7 What we ARE doing vs. what we AREN’T

Previous Voting results

Subject Matter Expertise Model(s) Current state polling results

Race

Gender

Urban vs rural population distribution

Total state population

Voter excitability

Education

Number of Russian bots on Twitter

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 8 What we ARE doing vs. what we AREN’T

Subject Matter Expertise Model(s) Simulation Model(s)

Data to Model

1. Individual state predictions

2. State Correlations

Simulation Results

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 9 Step 1: Mapping an election to a Boltzmann machine

!" #

1. http://www.fivethirtyeight.com AA BB AA BB Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 10

CC CC

Figure 2. (A) Example map of 538 state-by-state voting probabilitiesFigure 2. and(A) Examplethe resulting map national of 538 state probability.-by-state (B) voting State probabilitiesFigure 2. and(A) Examplethe resulting map national of 538 state probability.-by-state (B) voting State probabilitiesprobabilitiesFigure are 2.formed and(A) Examplethe from resulting a time map nationalseries of 538 averaging state probability.-by- statetechnique, (B) voting State andprobabilities (C) probabilitiesthe candidates are formed and lead the from translatesresulting a time national seriesinto an averaging overallprobability. probability. technique, (B) State andprobabilities (C) the candidates are formed lead from translates a time seriesinto an averaging overall probability. technique, andprobabilities (C) the candidates are formed lead from translates a time seriesinto an averaging overall probability. technique, and (C) the candidates lead translates into an overall probability. Available data is limited • What we would like: • Detailed breakdowns of demographics • Meticulously curated biases and correlations • All of the data that 538 has spent years and thousands of dollars curating

• What we have: • Publicly available results of previous US elections • State probabilities, as told by polls • Publicly accessible data from 538

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 11 Calculating the missing second order moments • In lieu of better curated data concerning second order moments, we calculated our own terms from previous US election results • Our methodology should not “break” first order moments

• Assumptions in this model: • In each previous election, if two states had the same election result, that increased their correlation • Elections that were more recent have a higher weight

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 12 Step 2: Mapping a Boltzmann machine to the QC

xi x j

The update equations for training the model: Potential quantum advantage 1 1 ∆%&' = − ,&,' − ,&,' ∆/& = − ,& - − ,& . A B + - . + A B AA BB Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 13

CC CC

Example of embedding a problem (left) into a fixed graph structure (right)1

1. Choi, Vicky. "Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design." arXiv preprint https://arxiv.org/pdf/1001.3116v2.pdf (2010).

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 14 Effect of embedding: Short qubit chains

• To validate the approach, we randomly chose first and second order terms for a hypothetical 5-state nation • Using the smallest embedding chains, this network was unable to properly train • “Hopfield” like results; optimal solutions rather than probabilistic results • Leads to huge changes in weights/biases, causing network instability

Diagonal = !" 1 Off diagonal = ! ! " 2 1

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 15 Effect of embedding: Long qubit chains

• For larger problem sizes, the embedding will necessarily have longer qubit chains • To simulate this for our small network, we artificially increased the qubit chains • With this approach, arbitrary first and second order moments were learned by the networks

Diagonal = !" 1 Off diagonal = ! ! " 2 1

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 16 Primary experiment • Goal: Using historical data and the QC-training methodology presented here, reproduce election forecasts over time • Some caveats: • Multiple models needed for modeling national error; 25 were used here • Limited time windows of D-Wave access, so results were generated every two weeks instead of daily • Limited hardware size made us omit 1 state and province (sorry Maryland and DC… you always vote D anyway) • For simplification, Maine and Nebraska were considered winner-take-all

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 17 Results – Training errors

Red lines = !" # Blue lines = !" 1

Examples testing extremes of correlations: negative, random, & positive

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 18 Results – Training errors

Large errors emerge when polls are updated and large changes occur

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2017 19 QC = Quantum trained Results – Training errors TB = National Trump bias CB = National Clinton bias

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2017 20 The most “impactful” states • Pearson correlation coefficients for the 10 states most (top) and least (bottom) correlated with the election forecasting results Our models 538

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 21 State errors • Individual states error distributions was highly dependent on if the state was a hard red, blue, or purple state

• Different ways of dealing with errors of this form: • Shimming • Multiple gauges

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 22 Summary • The QC-trained networks were able to learn structure in polling data to make election forecasts in line with the models of 538 • Trump was given a higher likelihood of victory (compared to other pollsters), even though the first order moments remained unchanged • Ideally in the future, we could rerun this method using correlations known with more detail in-house from 538 • Each iteration of the training model quickly produced 25,000 simulations (one for each national error model), which eclipses the 20,000 simulations 538 performs each time they rerun their models

Quantum Machine Learning for Election Modeling – Copyright QxBranch 2018 23 www.qxbranch.com | @qxbranch