| Title: | Quantum computing and the stable set problem |
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| Authors: | ID Krpan, Aljaž (Author)
ID Povh, Janez (Author)
ID Pucher, Dunja (Author) |
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| Files: |  URL - Source URL, visit https://www.tandfonline.com/doi/full/10.1080/10556788.2025.2490639
 PDF - Presentation file, download (2,71 MB)
MD5: FFA08541E4615E24ADFBC1D222DDDF75
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  RUDOLFOVO - Rudolfovo - Science and Technology Centre Novo Mesto
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| Abstract: | Given an undirected graph, the stable set problem asks to determine the cardinality of the largest subset of pairwise non-adjacent vertices. This value is called the stability number of the graph, and its computation is an NP-hard problem. In this paper, we solve the stable set problem using the D-Wave quantum annealer. By formulating the problem as a quadratic unconstrained binary optimization problem with the penalty method, we show its optimal value equals the graph's stability number for specific penalty values. However, D-Wave's quantum annealer is a heuristic, so the solutions may be far from the optimum and may not represent stable sets. To address these, we introduce a post-processing procedure that identifies samples that could lead to improved solutions. Additionally, we propose a partitioning method to handle larger instances that cannot be embedded on D-Wave's quantum processing unit. Finally, we investigate how different penalty parameter values affect the solutions' quality. Extensive computational results show that the post-processing procedure significantly improves the solution quality, while the partitioning method successfully extends our approach to medium-size instances. |
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| Keywords: | stable set problem, quantum annealing, graph partitioning, D-Wave |
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| Publication status: | In print |
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| Publication version: | Version of Record |
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| Submitted for review: | 22.05.2025 |
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| Article acceptance date: | 12.03.2025 |
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| Publication date: | 21.05.2025 |
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| Publisher: | Taylor & Francis Group |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 837-870 |
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| Numbering: | Vol. 40, iss. 4 |
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| PID: | 20.500.12556/DiRROS-23885  |
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| UDC: | 51 |
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| ISSN on article: | Y506-0494 |
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| DOI: | 10.1080/10556788.2025.2490639 |
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| COBISS.SI-ID: | 253384707 |
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| Copyright: | © 2025 The Author(s) |
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| Note: | Nasl. z nasl. zaslona;
Opis vira z dne 16. 10. 2025;
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| Publication date in DiRROS: | 13.11.2025 |
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| Views: | 187 |
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| Downloads: | 94 |
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| Metadata: |    |
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