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Title: Finding Maximum Cliques on the D-Wave Quantum Annealer

Abstract

This work 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.

Authors:
 [1]; ORCiD logo [1];  [2]; ORCiD logo [3]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Lancaster Univ. (United Kingdom). Dept. of Mathematics and Statistics Fylde College
  3. 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):
LA-UR-17-27718
Journal ID: ISSN 1939-8018
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Signal Processing Systems
Additional Journal Information:
Journal Volume: 91; Journal ID: ISSN 1939-8018
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Maximum clique; Quantum annealing; D-Wave 2X; Optimization; Gurobi

Citation Formats

Chapuis, Guillaume, Djidjev, Hristo, Hahn, Georg, and Rizk, Guillaume. Finding Maximum Cliques on the D-Wave Quantum Annealer. United States: N. p., 2018. Web. doi:10.1007/s11265-018-1357-8.
Chapuis, Guillaume, Djidjev, Hristo, Hahn, Georg, & Rizk, Guillaume. Finding Maximum Cliques on the D-Wave Quantum Annealer. United States. doi:10.1007/s11265-018-1357-8.
Chapuis, Guillaume, Djidjev, Hristo, Hahn, Georg, and Rizk, Guillaume. Thu . "Finding Maximum Cliques on the D-Wave Quantum Annealer". United States. doi:10.1007/s11265-018-1357-8. https://www.osti.gov/servlets/purl/1438358.
@article{osti_1438358,
title = {Finding Maximum Cliques on the D-Wave Quantum Annealer},
author = {Chapuis, Guillaume and Djidjev, Hristo and Hahn, Georg and Rizk, Guillaume},
abstractNote = {This work 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.},
doi = {10.1007/s11265-018-1357-8},
journal = {Journal of Signal Processing Systems},
number = ,
volume = 91,
place = {United States},
year = {2018},
month = {5}
}

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