Finding Maximum Cliques on the DWave Quantum Annealer
Abstract
This work 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.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Lancaster Univ. (United Kingdom). Dept. of Mathematics and Statistics Fylde College
 French Inst. for Research in Computer Science and Automation (INRIA) and Inst. for Research in Computer Science and Random Systems (IRISA), Rennes Cedex (France)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1438358
 Report Number(s):
 LAUR1727718
Journal ID: ISSN 19398018
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Signal Processing Systems
 Additional Journal Information:
 Journal Volume: 91; Journal ID: ISSN 19398018
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Maximum clique; Quantum annealing; DWave 2X; Optimization; Gurobi
Citation Formats
Chapuis, Guillaume, Djidjev, Hristo, Hahn, Georg, and Rizk, Guillaume. Finding Maximum Cliques on the DWave Quantum Annealer. United States: N. p., 2018.
Web. doi:10.1007/s1126501813578.
Chapuis, Guillaume, Djidjev, Hristo, Hahn, Georg, & Rizk, Guillaume. Finding Maximum Cliques on the DWave Quantum Annealer. United States. doi:10.1007/s1126501813578.
Chapuis, Guillaume, Djidjev, Hristo, Hahn, Georg, and Rizk, Guillaume. Thu .
"Finding Maximum Cliques on the DWave Quantum Annealer". United States. doi:10.1007/s1126501813578. https://www.osti.gov/servlets/purl/1438358.
@article{osti_1438358,
title = {Finding Maximum Cliques on the DWave Quantum Annealer},
author = {Chapuis, Guillaume and Djidjev, Hristo and Hahn, Georg and Rizk, Guillaume},
abstractNote = {This work 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.},
doi = {10.1007/s1126501813578},
journal = {Journal of Signal Processing Systems},
number = ,
volume = 91,
place = {United States},
year = {2018},
month = {5}
}
Web of Science
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