Finding Maximum Cliques on the DWave Quantum Annealer
Abstract
This paper assesses the performance of the DWave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NPhard 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 thirdparty clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical postprocessing 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 speedups in computing time over classical approaches.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 arXiv:
 arXiv:1801.08649
 Bibcode:
 2018arXiv180108649C
 Keywords:

 Quantum Physics
 EPrint:
 ACM Intl Conference on Computing Frontiers 2017