1 © Copyright 2007 D-Wave Systems, Inc. Progress in Quantum Computing panel presentation slides Supercomputing 2007 Reno, Nevada November 15 th, 2007 1:30pm—3:00pm

1 © Copyright 2007 D-Wave Systems, Inc.

Progress in Quantum Computing panel presentation slides

Supercomputing 2007 Reno, Nevada

November 15th, 2007 1:30pm—3:00pm

Image matching with a 28-qubitsuperconducting quantum computer


Image matching technical leads

• Image matching algorithms and applications

Dr. Hartmut Neven, Technical Lead Manager

[email protected]

• Quantum computing algorithms and hardware

Dr. Geordie Rose, Chief Technology Officer

[email protected]


Prologue: D-Wave

• Only pure play company in two categories: quantum computation and superconducting computing systems

• Best financed & largest effort in both categories

• More granted US QC patents than all other corporations (IBM, Microsoft, HP, NEC, …) combined

• Empirical high-throughput philosophy; Eight full processor design cycles completed so far in 2007

• Core technical team TRW, NASA, JPL, MDA, Kodak, Electronic Arts, LSI Logic, top computer science & physics research scientists


Overview

• Our system: The problem we solve

• How superconducting AQCs work: Some physics

• Case study: Solving image matching problems with a D-Wave quantum computing system


Demo system is a web services QUBO solver

•Quadratic Unconstrained Binary Optimization: Minimize E over binary variables xi ; hi & Jij

N

jijiij

N

iiiN xxJxhxxE

111 ),,(


High-level systems architecture

User data

Local solver engine Quantum computer

QUBO out

Solution returned

Jh ˆ,

x


Under the Hood:

D-Wave quantum processors


A problem with a split personality

•QUBO is equivalent to the two-dimensional Ising model in a magnetic field (2DIMM) problem


What this problem means to a computer scientist

•QUBO is NP-hard ; the decision version is NP-complete

Few technical terms have gained such rapid notoriety as the appellation “NP-complete”. In the short time since its introduction in the early 1970s, this term has come to symbolize the abyss of inherent intractability that algorithm designers increasingly face as they seek to solve larger and more complex problems.

Computers and Intractability: A Guide to the Theory of NP-CompletenessMichael R. Garey and David S. Johnson


The Ising model tries to imitate behaviour in which individual elements (e.g., atoms, animals, protein folds, biological membrane, social behavior, etc.) modify their behavior so as to conform to the behavior of other individuals in their vicinity… More than 12,000 papers have been published between 1969 and 1997 using the Ising model.

http://scienceworld.wolfram.com/physics/IsingModel.html

What this problem means to a physicist

•Model for describing real physical systems


Core concept: Use (quantum) physics to do math

•Deep connection between hard math problem and fundamental laws of nature

•Build an “analog computer” at the ultimate limits of what is possible… any computer that could do better would violate the laws of physics

Math

Physics


Our approach: Superconducting adiabatic quantum computer

• Extremely fast: Special purpose processor; superconducting electronics are naturally fast (700+ GHz)

• Extremely low power: In principle reversible (zero heat generation); in practice power consumption & heat generation drastically reduced (factors of millions)

•At the limits of physics: Universal quantum computer… can’t do better


Device schematic: Niobium CJJ RF-SQUID flux qubit

Qubit loopCompound Josephson junction (CJJ) loop

Two currents in

c x One current out



H 0Iccos

c

2cos

02

8 2L x 2 2e

2

C

2

2

Potential energy: cosine + parabola

Device physics: The Hamiltonian


2

222

2

200 2

8cos

2cos

C

e

L

IH x

cc

Potential energy can be programmed by user

E


Qubit manipulation: c modulates barrier height


Qubit manipulation: x tilts double well


xczx tthtH |0> |1>

Readout basis: Direction of circulating current


Device schematic: Symmetric bipolar coupler



Models of computation:\\adiabatic quantum computation

• Computer initialized in “easy to reach” (convex) ground state

• Answer encoded in final state

• All currents adjusted slowly enough so that system remains in ground state at all times

• AQC can be universal for QC

• AQC is exact by definition

PB HsHsH 1


Models of computation:\\quantum annealing

• Computer initialized in ground state

• Answer encoded in final state

• All currents adjusted over period of time fixed by user

• QA is a heuristic algorithm PB HsHsH 1


Processor designed to enable AQC/QA

28

,

28

1

28

1 Eji

jz

izij

iz

ii

ix

ii tJthttH


Problem Hamiltonian = desired QUBO

PB HsHsH 1

HB i

i1

N

xi

HP hii1

N

zi Jij z

i zj

i, jE

N

N

Eji

jz

izij

iz

N

ii

ix

N

ii tJthttH

,11


A simple operating prescription

1. Set CJJ biases to maximally lower barriers

2. Raise {h,J} biases to target values

3. Ramp CJJ biases to large barriers

4. Read out qubits

HB i

i1

N

xi

N

Eji

jz

izij

iz

N

ii

ix

N

ii tJthttH

,11

HP hii1

N

zi Jij z

i zj

i, jE

N


Image matching

• This is hard: Automated object recognition is a foundational artificial intelligence problem known to be very difficult for designed (as opposed to evolved) computers


Image matching

•Given two images


Image matching

• Identify interest points in each image


Image matching

•Generate local description of all interest points (local wavelet transform feature vectors)

03.0,,01.0,31.0

jrj


Image matching

•Define point-wise similarity between interest point j in image 1 and interest point in image 2 to be inner product of feature vectors

rrj

j


Image matching

•Generate relational description of all pairs of interest points

j

k

0,,05.0,22.0

jks


Image matching

•Define relational compatibility of a pair (j,k) from first image and a pair (,) from second image

ss jk


Image matching as a QUBO

•Quadratic Unconstrained Binary Optimization problem: Minimize E over binary variables x[ i, ]

• The set of all pairs {iG1,G2} where x[ i, ]=1 gives the region and size of maximum overlap

M

jiji

N

ij

M

ii

N

iMN xxssxrrxxE1

],[],[11

],[1

],[]1,1[ ),,(

Favors point-wise similarity Favors relational compatibility


Show Demo


Summary of preliminary results

•A set of progressively more powerful superconducting quantum processors have been built

•Next generation Q3/2008 targets competition with incumbent QUBO solver methods (500+ qubits)

•Web services architecture operational at several levels of abstraction from hardware; APIs documented and available

Documents

1 © Copyright 2007 D-Wave Systems, Inc. Progress in Quantum Computing panel presentation slides Supercomputing 2007 Reno, Nevada November 15 th, 2007 1:30pm—3:00pm