Quantum annealing - microsoft.com Department of Physics Institute for Theoretical Physics Quantum...
Transcript of Quantum annealing - microsoft.com Department of Physics Institute for Theoretical Physics Quantum...
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
DPHYSDepartment of Physics
Institute for Theoretical Physics
Beyond Moore’s law: quantum devices
2
Quantum randomnumber generators
Quantum simulators Quantum computer
?Windows Q
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
When will we have a quantum computer?
4
?Windows Q
Thursday, July 11, 13
\
May 2011:
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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.
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
May 2013: D-Wave is 3600x faster than classical computers!?
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Experimental Evaluation of an Adiabiatic Quantum Systemfor Combinatorial Optimization
Catherine C. McGeoch
Amherst College
Amherst MA, USA
Cong Wang
Simon Fraser University
Burnaby BC, CA
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.
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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 ...”
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
Some magazines investigate deeper ...
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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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Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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
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Does it work?
Is it quantum or classical?
Is it thousands of times faster than anything classical?
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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)
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aijij∑ xix j + bi
i∑ xi where xi ∈{0,1}
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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}
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
Annealing and simulated annealing
Annealing
A 7000 year old neolithic technology
Slowly cool a metal to improve its properties
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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
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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
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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
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
The D-Wave device
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Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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
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Credit: D-Wave Systems
Jijij∑ xix j + hi
i∑ xi
Thursday, July 11, 13
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
DPHYSDepartment of Physics
Institute for Theoretical Physics
Lockheed Martin bought two D-Wave devices
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Jijij∑ xix j + hi
i∑ xi
Couplings can be definedon edges of the“chimera graph” implemented by the device
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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
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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
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
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
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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
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
Success probability histograms
D-Wave One is inconsistent with a classical annealerD-Wave One is consistent with a simulated quantum annealer
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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
Thursday, July 11, 13
The same instances are hard and easy on D-Wave and the simulated quantum annealer
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
Correlations between D-Wave and a simulated quantum annealer
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hard for both D-Wave andthe simulated quantum annealer
easy for both D-Wave andthe simulated quantum annealer
Thursday, July 11, 13
Matthias Troyer
DPHYSDepartment of Physics
Institute for Theoretical Physics
Scaling of the median time to solution with problem size
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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
Thursday, July 11, 13
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
DPHYSDepartment of Physics
Institute for Theoretical Physics
We understand the D-Wave “black box” much better
24
aijij∑ xix j + bi
i∑ xi
Thursday, July 11, 13