Table Of Content

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 ©2016D-WaveSystemsInc.Allrightsreserved. 2/27 D-Wave QPU (cid:73) Quantumannealingchip (cid:73) Highlyspecializedco-processor (cid:73) Physicalimplementationofan NP-hardoptimizationproblem (cid:73) Physicalheuristicalgorithmruns onthechip ©2016D-WaveSystemsInc.Allrightsreserved. 3/27 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 ©2016D-WaveSystemsInc.Allrightsreserved. 4/27 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 ©2016D-WaveSystemsInc.Allrightsreserved. 5/27 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) ©2016D-WaveSystemsInc.Allrightsreserved. 6/27 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) ©2016D-WaveSystemsInc.Allrightsreserved. 7/27 Motivation for GPU Solvers ©2016D-WaveSystemsInc.Allrightsreserved. 8/27 Why develop optimized GPU implementations? (cid:73) Quantumcomputersare hardtosimulate (cid:73) Evenapproximate simulationsviaMonte Carlomethodscanbeslow Betweensome quantilesandsystem sizesweobservea prefactoradvantage [forD-Wave]ashigh as108. -Denchevetal.(2015) ©2016D-WaveSystemsInc.Allrightsreserved. 9/27 Why develop optimized GPU implementations? (cid:73) Softwaresolversslowdownourexperiments ”Thisexperimentoccupiedmillionsofprocessorcores forseveraldaystotuneandruntheclassical algorithmsforthesebenchmarks.” -Denchevetal.(2015) (cid:73) Fastersolvers→fasterexperimentalcycle→improved understandingofourchips (cid:73) FastGPUsimulationleadstobetterquantumcomputers! ©2016D-WaveSystemsInc.Allrightsreserved. 10/27

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