Finding Maximum Cliques on a Quantum Annealer

Chapuis, Guillaume and Djidjev, Hristo and Hahn, Georg and Rizk, Guillaume (2017) Finding Maximum Cliques on a Quantum Annealer. In: CF'17 Proceedings of the Computing Frontiers Conference. Association for Computing Machinery, Inc, ITA, pp. 63-70. ISBN 9781450344876

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This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, and compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.

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© ACM, 2017. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in CF'17 Proceedings of the Computing Frontiers Conference
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24 Apr 2018 12:40
Last Modified:
19 Sep 2020 07:07