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Finding Maximum Cliques on the D-Wave Quantum Annealer
Open accessAbstract
This paper 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.
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A comparison between various decomposition techniques has demonstrated the superiority of qbsolv in terms of solution quality.
“Acomparison between various decomposition techniques, i.e., principal component decomposition [185], free-and-anneal [163], qbSolv, and iterative centrality halo [172] has demonstrated the superiority of qbsolv in terms of solution quality [12].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [172]
Section 3.1.2 describes qbSolv as a tool for splitting large QUBO problems, but our copy does not compare its solution quality with principal component decomposition, free-and-anneal, or iterative centrality halo. Section 4.2 says every solver in its small-graph experiment found a maximum clique; that experiment does not establish the claimed superiority. Searches for the named techniques and comparative solution quality found no such assessment. (LLM, conf=0.76)
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Metadata
- Authors
- Chapuis, G., Djidjev, H., Hahn, G., & Rizk, G.
- Affiliations
- Los Alamos National Laboratory (US)
- Lancaster University (GB)
- Institut national de recherche en sciences et technologies du numérique (FR)
- Corresponding author
- Hahn, Georg
- Venue
- Journal of Signal Processing Systems
- Published
- 2018-05-03
- Volume
- 91
- Issue
- 3-4
- Pages
- 363-377
- ISSN
- 1939-8018 (ISSN-L)
- 1939-8115
- OpenAlex
- W2786959618
- Cited by
- 70
- References
- 30
- Citations by year
- 2025: 3 · 2024: 6 · 2023: 11 · 2022: 16 · 2021: 12 · 2020: 13 · 2019: 8 · 2018: 1
- FWCI
- 4.72
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of Signal Processing Systems (publishedVersion, cc-by)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- HAL (submittedVersion, other-oa)
- Funders
- Laboratory Directed Research and Development
- Los Alamos National Laboratory
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Keywords
- maximum clique problem, D-Wave quantum annealer, quantum annealing, QUBO formulation, NP-hard combinatorial optimization, simulated annealing comparison, quantum advantage, classical post-processing, random graphs
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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