Finding Maximum Cliques on the D-Wave Quantum Annealer

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg; Rizk, Guillaume

doi:10.1007/s11265-018-1357-8

Finding Maximum Cliques on the D-Wave Quantum Annealer

Journal Article · Thu May 03 00:00:00 EDT 2018 · Journal of Signal Processing Systems

DOI:https://doi.org/10.1007/s11265-018-1357-8· OSTI ID:1438358

Chapuis, Guillaume ^[1]; ^[1]; Hahn, Georg ^[2]; ^[3]

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)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1438358

Report Number(s):: LA-UR--17-27718

Journal Information:: Journal of Signal Processing Systems, Journal Name: Journal of Signal Processing Systems Vol. 91; ISSN 1939-8018

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Picking Efficient Portfolios from 3,171 US Common Stocks with New Quantum and Classical Solvers Cohen, Jeffrey; Alexander, Clark arXiv https://doi.org/10.48550/arxiv.2011.01308	preprint	January 2020
Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models Glover, Fred; Kochenberger, Gary; Du, Yu 4OR, Vol. 17, Issue 4 https://doi.org/10.1007/s10288-019-00424-y	journal	November 2019

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