Quantum annealing - microsoft.com Department of Physics Institute for Theoretical Physics Quantum annealing Matthias Troyer (ETH Zürich) John Martinis (UCSB) Dave Wecker (Microsoft)

DPHYSDepartment of Physics

Institute for Theoretical Physics

Quantum annealingMatthias Troyer (ETH Zürich)John Martinis (UCSB)Dave Wecker (Microsoft)

Troels Rønnow (ETH)Sergei Isakov (ETH →Google)Lei Wang (ETH)

Sergio Boixo (USC → Google)Daniel Lidar (USC) Zhihui Wang (USC)

Thursday, July 11, 13

Disruptive technology change: use quantum mechanics for computing!

Matthias Troyer



Beyond Moore’s law: quantum devices

2

Quantum randomnumber generators

Quantum simulators Quantum computer

?Windows Q


Matthias Troyer



Quantum random number generators

3

0 1photo detectors

photon source

semi-transparent mirror

0

Create true random numbers using the laws of quantum mechanics

1. Photon source emits a photon

2. Photon hits semitransparent mirror

3. Photon follows both paths

4. The photo detectors see the photon only in one place: random selection


Matthias Troyer



When will we have a quantum computer?

4

?Windows Q


\

May 2011:


From http://www.dwavesys.com


http://www.dwavesys.com


From http://www.dwavesys.com




Matthias Troyer



8

Friday, March 22, 2013

(page 1) .... if it performs as Lockheed and D-Wave expect, the design could be used to supercharge even the most powerful systems, solving some science and business problems millions of times faster than can be done today.

(page 2) However, ... scientists have not yet published scientific data showing that the system computes faster than today’s conventional binary computers. ... critics of D-Wave’s method say it is not quantum computing at all, but a form of standard thermal behavior.


Matthias Troyer



May 2013: D-Wave is 3600x faster than classical computers!?

9

Experimental Evaluation of an Adiabiatic Quantum Systemfor Combinatorial Optimization

Catherine C. McGeoch

Amherst College

Amherst MA, USA

[email protected]

Cong Wang

Simon Fraser University

Burnaby BC, CA

[email protected]

ABSTRACTThis paper describes an experimental study of a novel com-puting system (algorithm plus platform) that carries outquantum annealing, a type of adiabatic quantum computa-tion, to solve optimization problems. We compare this sys-tem to three conventional software solvers, using instancesfrom three NP-hard problem domains. We also describeexperiments to learn how performance of the quantum an-nealing algorithm depends on input.

Categories and Subject DescriptorsC.4 [Computer Systems Organization]: Performance ofSystems; F.2 [Theory of Computation]: Analysis of Al-gorithms and Problem Complexity

General TermsAlgorithms, Experimentation, Performance

KeywordsAdiabatic Quantum Computing, Quantum Annealing, D-Wave, Heuristics

1. INTRODUCTIONAdiabatic quantum computation (AQC),1 proposed in 2000

by Farhi et al. [17], represents a new model of computationas well as a new paradigm in algorithm design. The com-putational model is polynomially equivalent to the better-known quantum gate model [1], [18], [33]. Theoretical anal-ysis of specific AQC algorithms has returned mixed resultsto date, with indications of exponential speedups and some-times slowdowns over conventional algorithms.

This paper presents an experimental study of algorithmsbased on quantum annealing (a type of AQC computation),

1The term “adiabatic” in this context refers to a quan-tum process where no population exchange between allowedstates of the system occurs.

Permission to make digital or hard copies of all or part of this work for

personal or classroom use is granted without fee provided that copies are

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bear this notice and the full citation on the first page. To copy otherwise, to

republish, to post on servers or to redistribute to lists, requires prior specific

permission and/or a fee.

CF’13, May 14–16, 2013, Ischia, Italy.

Copyright 2013 ACM 978-1-4503-2053-5 ...$15.00.

running on a special-purpose D-Wave Two platform2 con-taining 439 quantum bits (qubits). Earlier systems withbetween 84 and 108 qubits have been used for finding Ram-sey numbers [4], binary classification in image matching [28],and 3D protein folding [29].The “native” problem for this system is a restriction – to

Chimera-structured inputs defined in Section 2 – of the IsingSpin Model (IM). Native instances can be solved directlyon the quantum hardware (QA), while general inputs aresolved by a hybrid approach (called Blackbox) that alter-nates heuristic search with hardware queries.We report on two experimental projects. First, QA and

Blackbox are compared to three conventional software solvers:CPLEX [23], METSlib tabu search (TABU) [27], and abranch-and-bound solver called Akmaxsat (AK) [26] . Thesolvers are evaluated using instances from three NP-Hardproblems: Quadratic Unconstrained Binary Optimization(QUBO); Weighed Maximum 2-Satisfiability (W2SAT), andthe Quadratic Assignment Problem (QAP).In horserace terms, QA dominates on the Chimera-structure

QUBO problems: at the largest problem size n = 439,CPLEX (best among the software solvers), returns compa-rable results running about 3600 times slower than the hard-ware. On the W2SAT problems, Blackbox, AK, and TABUall find optimal solutions within the same time frame. Onthe QAP problems, Blackbox finds best solutions in 28 of 33cases, compared to 9 cases for TABU (the next-best solveron these inputs).Note that these results can be regarded as “snapshots” of

performance for specific implementations on specific inputsets, nothing more. Experimental studies of heuristics arenotoriously di�cult to generalize. Furthermore – unlike ex-periments in the natural sciences – no experimental assess-ment of heuristic performance can be considered final, sinceperformance is a moving target that improves over time asnew ideas are incorporated into algorithms and code. Futureresearch will likely turn up better solvers and strategies.As a case in point, our second project compares the V5

hardware chip used in our first study to a V6 chip thatbecame operational after the study was completed. V6 isthree to five times faster than V5, and can solve problemsas large as n = 502.

2Manufactured by D-Wave Systems Inc., BC, Canada. Wethank D-Wave sta↵ for their generous assistance in set-ting up experiments, collecting data, and helping us to un-derstand AQC and quantum annealing: Zhengbing Bian,Fabian Chudak, Suzanne Gildert, Mani Ranjbar, GeordieRose, Murray Thom, and Dominic Walliman.

Special purpose heuristic device (D-Wave) needs 0.491s

General purpose exact solver (CPLEX) needs 30 minutes on one CPU core

“It would of course be interesting to see if highly tuned implementations could compete ...”


Matthias Troyer



Some magazines investigate deeper ...

10

5/29/13 5:37 AMQuantum computing: Faster, slower—or both at once? | The Economist

Page 1 of 3http://www.economist.com/news/science-and-technology/21578027-fi…rld-contests-between-quantum-computers-and-standard-ones-faster

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May 18th 2013 | From the print edition

Quantum computing

Faster, slower—or both at once?The first real-world contests between quantum computers and standard ones

CHIPMAKERS dislike quantum mechanics.Half a century of Moore’s law means theirproducts have shrunk to the point wherethey are subject to the famous weirdness ofthe quantum world. That makes designingthem difficult. Happily, those samequantum oddities can be turned intofeatures rather than bugs. For many yearsresearchers have been working oncomputers that would rely on the strangelaws of quantum mechanics to do usefulcalculations. They would do this by usingbinary digits which, instead of having avalue of either “one” or “zero”, had both atthe same time. That might allow them to dosome calculations much faster than non-quantum, “classical” computers can manage.

Progress has been slow, but steady. And now it may be possible to see how a certaintype of quantum computer performs in the real world. On May 15th, at a computingconference in Ischia in Italy, Catherine McGeoch, a computer scientist at AmherstCollege in Massachusetts, presented a paper describing the performance of a quantumcomputer manufactured by a Canadian firm called D-Wave.

D-Wave has a colourful history. To much fanfare and pressattention (including in The Economist), it announced aworking quantum computer in 2007. Sporting asuperconducting chip cooled to within a fraction of a degreeof absolute zero, this certainly sounded high-tech. But thefirm provided little concrete information, and given how farahead it seemed to be compared with academic laboratoriesworking on the same problem, many computer scientistswere sceptical of its claim to have created a truly quantummachine. Following the publication of a paper in Nature in2011, however, it is now generally accepted that the firmhas built a working version of a specific type of machinecalled an adiabatic quantum computer.

Unlike a “standard” quantum computer, which (if one is everbuilt) could answer the same sorts of question that aclassical computer can, an adiabatic computer is limited to a

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Matthias Troyer



What is behind this?

D-Wave is not a universal quantum computer but a special purpose quantum optimizer

We performed experiments on D-Wave devices to answer these questions

11

Does it work?

Is it quantum or classical?

Is it thousands of times faster than anything classical?


Matthias Troyer



Binary quadratic optimization: an NP-hard problem

Find the values xi (=0 or 1) which minimize the quadratic cost function

Finding the solution is exponentially hard (unless P=NP)

12

aijij∑ xix j + bi

i∑ xi where xi ∈{0,1}


Matthias Troyer



The Ising spin glass: an NP-hard problem

Find the values xi (= -1 or +1) which minimize the quadratic cost function

Finding the solution is exponentially hard (unless P=NP)

Many important problems can be expressed as binary quadratic optimization problems (or Ising spin glasses) with only polynomial overhead

factoring integers: 15 = 3 x 5traveling salesman problemportfolio optimizationgraph isomorphism...

Can a quantum device solve these problems faster than a classical one?13

Jijij∑ xix j + hi

i∑ xi where xi ∈{−1,+1}


Matthias Troyer



Annealing and simulated annealing

Annealing

A 7000 year old neolithic technology

Slowly cool a metal to improve its properties

14

Simulated annealingKirkpatrick, Gelatt and Vecchi, Science (1983)

A 30 year old optimization technique

Slowly cool a model in a Monte Carlo simulationto find the solution to an optimization problem

We don’t always find the global minimum and have to try many times


Matthias Troyer



Quantum annealing

Advantages of quantum mechanics

A quantum particle can be everywhere at onceand explore all of the configuration space

Quantum annealing schedule

Start with a constant potential V(x)

The particle is everywhere with equal probabilitygiven by the square of the wave function

Turning on the potential the wave functionconcentrates around the minima of the potential

15

V (x)

Ψ(x) 2

Ψ(x) 2

We have to anneal very slowly for the hard problemsto let the particle “tunnel” to the global minimum


Matthias Troyer



The D-Wave device

16


Matthias Troyer



Superconducting flux qubits

The qubit is implemented bymagnetic fluxes caused bycirculating superconducting currents

0: magnetic flux flowing down

1: magnetic flux flowing up

Programmable magnetic couplingallows to define the optimization problem

17

Credit: D-Wave Systems

Jijij∑ xix j + hi

i∑ xi


D-Wave One installed at USC in October 2011: 108 of 128 qubits workingD-Wave Two installed at USC in March 2013: 503 of 512 qubits working

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1Matthias Troyer



Lockheed Martin bought two D-Wave devices

18

Jijij∑ xix j + hi

i∑ xi

Couplings can be definedon edges of the“chimera graph” implemented by the device


Matthias Troyer



Is D-Wave a quantum annealer?

Hypothesis 1: D-Wave is a not quantum but

just a classical annealer

Hypothesis 2: D-Wave is a quantum annealer

Hypothesis 3: D-Wave is a quantum deviceand shows quantum speedup

19

Experimental test: compare to a simulated classical annealer

(Monte Carlo simulation)

Experimental test: compare to a simulated quantum annealer

(quantum Monte Carlo)

Experimental test: scaling with problem size is better than that

of the classical codes

Many scientists doubt that D-Wave is a quantum device since the qubits are imperfect and the device is exposed to lots of thermal noise


Matthias Troyer



The experiments to test the machine

Find the hardest problems that the machine can solve Random ±1 couplings on all edges of the chimera graph

20

hundred million experimentson D-Wave One

billions of simulationsclassical and quantum Monte Carlo

1000s of choices of couplings 1000s of repetitions of the annealing

10s of problem sizesvary the annealing time and schedule


Matthias Troyer



Success probability histograms

D-Wave One is inconsistent with a classical annealerD-Wave One is consistent with a simulated quantum annealer

21

Simulatedclassical annealer

Simulated quantum annealer

D-Wave One

1. Pick 1000 different random problems2. For each problem run experiments and count how often the global minimum was reached3. Plot a histogram of the probabilities of finding the global minimum


The same instances are hard and easy on D-Wave and the simulated quantum annealer

Matthias Troyer



Correlations between D-Wave and a simulated quantum annealer

22

hard for both D-Wave andthe simulated quantum annealer

easy for both D-Wave andthe simulated quantum annealer


Matthias Troyer



Scaling of the median time to solution with problem size

23

D-Wave One

Belief Propagation (exact)

Simulated Quantum Annealing

Simulated Annealing

generic

optimizedparallelizedGPU

D-Wave Two 200 Monte Carlo updatesper nanosecond

This is for random ±1 couplings and the conclusion may be different for other benchmarks


Special purpose device for combinatorial optimization problems

Finds the global optimum out of 2503 states (non-trivial!)

Evidence for quantum behaviorPerformance correlates well with a simulated quantum annealer but not with a simulated classical annealer

Performance can (so far) be matched by highly optimized classical codes on a single GPU or CPU

Observed scaling is the same as that of classical codes

Can improved calibration change the conclusion?

Matthias Troyer



We understand the D-Wave “black box” much better

24

aijij∑ xix j + bi

i∑ xi


Documents

Quantum annealing - microsoft.com Department of Physics Institute for Theoretical Physics Quantum annealing Matthias Troyer (ETH Zürich) John Martinis (UCSB) Dave Wecker (Microsoft)