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:
-
- 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 Laboratory (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. https://doi.org/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. https://doi.org/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 = {Thu May 03 00:00:00 EDT 2018},
month = {Thu May 03 00:00:00 EDT 2018}
}
Web of Science
Works referenced in this record:
Fast algorithms for determining (generalized) core groups in social networks
journal, November 2010
- Batagelj, Vladimir; Zaveršnik, Matjaž
- Advances in Data Analysis and Classification, Vol. 5, Issue 2
Traffic Flow Optimization Using a Quantum Annealer
journal, December 2017
- Neukart, Florian; Compostella, Gabriele; Seidel, Christian
- Frontiers in ICT, Vol. 4
Finding a Maximum Clique in an Arbitrary Graph
journal, November 1986
- Balas, Egon; Yu, Chang Sung
- SIAM Journal on Computing, Vol. 15, Issue 4
Defining and detecting quantum speedup
journal, June 2014
- Ronnow, T. F.; Wang, Z.; Job, J.
- Science, Vol. 345, Issue 6195
Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor
journal, August 2014
- Bunyk, P. I.; Hoskinson, Emile M.; Johnson, Mark W.
- IEEE Transactions on Applied Superconductivity, Vol. 24, Issue 4
A simple simulated annealing algorithm for the maximum clique problem
journal, November 2007
- Geng, Xiutang; Xu, Jin; Xiao, Jianhua
- Information Sciences, Vol. 177, Issue 22
Quantum annealing with manufactured spins
journal, May 2011
- Johnson, M. W.; Amin, M. H. S.; Gildert, S.
- Nature, Vol. 473, Issue 7346
Graph Partitioning using Quantum Annealing on the D-Wave System
conference, January 2017
- Ushijima-Mwesigwa, Hayato; Negre, Christian F. A.; Mniszewski, Susan M.
- Proceedings of the Second International Workshop on Post Moores Era Supercomputing - PMES'17
Fast clique minor generation in Chimera qubit connectivity graphs
journal, October 2015
- Boothby, Tomas; King, Andrew D.; Roy, Aidan
- Quantum Information Processing, Vol. 15, Issue 1
Solving Set Cover with Pairs Problem using Quantum Annealing
journal, September 2016
- Cao, Yudong; Jiang, Shuxian; Perouli, Debbie
- Scientific Reports, Vol. 6, Issue 1
Quantum versus simulated annealing in wireless interference network optimization
journal, May 2016
- Wang, Chi; Chen, Huo; Jonckheere, Edmond
- Scientific Reports, Vol. 6, Issue 1
Pakistan and India Relations: A Political Analysis of Conflicts and Regional Security in South Asia
journal, December 2016
- Yaseen, Zahid; Jathol, Iqra; Muzaffar, Muhammad
- Global Political Review, Vol. 1, Issue 1
Test case generators and computational results for the maximum clique problem
journal, January 1993
- Hasselberg, Jonas; Pardalos, Panos M.; Vairaktarakis, George
- Journal of Global Optimization, Vol. 3, Issue 4
What is the Computational Value of Finite Range Tunneling?
text, January 2015
- Denchev, Vasil S.; Boixo, Sergio; Isakov, Sergei V.
- arXiv
Graph Partitioning using Quantum Annealing on the D-Wave System
preprint, January 2017
- Ushijima-Mwesigwa, Hayato; Negre, Christian F. A.; Mniszewski, Susan M.
- arXiv
Works referencing / citing this record:
Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models
journal, November 2019
- Glover, Fred; Kochenberger, Gary; Du, Yu
- 4OR, Vol. 17, Issue 4
A maximum edge-weight clique extraction algorithm based on branch-and-bound
journal, August 2020
- Shimizu, Satoshi; Yamaguchi, Kazuaki; Masuda, Sumio
- Discrete Optimization, Vol. 37
Picking Efficient Portfolios from 3,171 US Common Stocks with New Quantum and Classical Solvers
preprint, January 2020
- Cohen, Jeffrey; Alexander, Clark
- arXiv