Simulating a quantum annealer with GPU-based Monte Carlo algorithms

27 Pages·2016·2.36 MB·English

Simulating a quantum annealer with
GPU-based Monte Carlo algorithms
Mayssam Mohammadi Nevisi
Mani Ranjbar
James King
Sheir Yarkoni
Jeremy P. Hilton
Catherine C. McGeoch
April6,2016
Introduction
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D-Wave QPU
(cid:73) Quantumannealingchip
(cid:73) Highlyspecializedco-processor
(cid:73) Physicalimplementationofan
NP-hardoptimizationproblem
(cid:73) Physicalheuristicalgorithmruns
onthechip
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Ising Minimization
Given:
(cid:73) AgraphG=(V,E)
(cid:73) Acollectionofweightsh={h :i ∈V}and
i
J ={J :(i,j)∈E}(theHamiltonian)
ij
Assign:
(cid:73) Valuesfrom{−1,+1}tonspinvariabless ={s}
i
Suchthatweminimizetheenergyfunction:
(cid:88) (cid:88)
E(s)= hs + J ss.
i i ij i j
i∈V (i,j)∈E
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Chimera topology
(cid:73) C isak ×k gridofdenseK
k 4,4
“unitcells”
Processor Topology Qubits
D-WaveOne C 128
4
D-WaveTwo C 512
8
D-Wave2X C 1152
12
(cid:73) Chimeratopologiesarebipartite
(cid:73) Anygraphcanbeembeddedin
aChimeragraphviaminor
embedding
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Simulated (Thermal) Annealing
(cid:73) Heuristicoptimizationalgorithm Thermal Jump
thatsimulatesclassicalthermal
annealing
(cid:73) Systemofspinsmovesrandomly
instatespace Energy
(cost)
(cid:73) Coolsslowlyfromhot
(random/explorative)tocold
(greedy/exploitative)
(cid:73) Usesthermalactivationtojump
Configuration
overenergybarriers (state)
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Quantum Annealing
(cid:73) Quantumannealing(QA)is Thermal Jump
relatedtoadiabaticquantum
computing(AQC)
H(t)=A(t)·H +B(t)·H .
init prob
Energy
(cost)
(cid:73) Takesadvantageofthermal Quantum
Tunneling
activationjustlikeclassical
annealing
(cid:73) Alsohasanewcomplementary
Configuration
resource: quantumtunneling. (state)
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Motivation for GPU Solvers
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Why develop optimized GPU implementations?
(cid:73) Quantumcomputersare
hardtosimulate
(cid:73) Evenapproximate
simulationsviaMonte
Carlomethodscanbeslow
Betweensome
quantilesandsystem
sizesweobservea
prefactoradvantage
[forD-Wave]ashigh
as108.
-Denchevetal.(2015)
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Why develop optimized GPU implementations?
(cid:73) Softwaresolversslowdownourexperiments
”Thisexperimentoccupiedmillionsofprocessorcores
forseveraldaystotuneandruntheclassical
algorithmsforthesebenchmarks.”
-Denchevetal.(2015)
(cid:73) Fastersolvers→fasterexperimentalcycle→improved
understandingofourchips
(cid:73) FastGPUsimulationleadstobetterquantumcomputers!
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