ebook img

Simulating a quantum annealer with GPU-based Monte Carlo algorithms PDF

27 Pages·2016·2.36 MB·English
by  
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Simulating a quantum annealer with GPU-based Monte Carlo algorithms

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

Description:
April 6, 2016. Page 2. ©2016 D-Wave Systems Inc. All rights reserved. Introduction. 2 / 27 Physical heuristic algorithm runs on the chip. 3 / 27
See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.