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Epping, Michael and Stollenwerk, Tobias (2021) A Measurement-based Algorithm for Graph Colouring. Quantum. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. ISSN 2521-327X. (Submitted)
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Abstract
We present a novel algorithmic approach to find a proper vertex colouring of a graph with d colours, if it exists. We associate a d-dimensional quantum system with each vertex and the initial state is a mixture of all possible colourings, from which we obtain a random proper colouring of the graph by measurements. The non-deterministic nature of the quantum measurement is tackled by a reset operation, which can revert the effect of unwanted projections. As in the classical case, we find that the runtime scales exponentially with the number of vertices. However, we provide numerical evidence that the average runtime for random graphs scales polynomially in the number of edges.
| Item URL in elib: | https://elib.dlr.de/148460/ | |||||||||
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| Document Type: | Article | |||||||||
| Title: | A Measurement-based Algorithm for Graph Colouring | |||||||||
| Authors: |
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| Date: | 2021 | |||||||||
| Journal or Publication Title: | Quantum | |||||||||
| Refereed publication: | No | |||||||||
| Open Access: | Yes | |||||||||
| Gold Open Access: | Yes | |||||||||
| In SCOPUS: | Yes | |||||||||
| In ISI Web of Science: | Yes | |||||||||
| Publisher: | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften | |||||||||
| ISSN: | 2521-327X | |||||||||
| Status: | Submitted | |||||||||
| Keywords: | Algorithmus, Graphfärbung, Quantenalgorithmus | |||||||||
| HGF - Research field: | other | |||||||||
| HGF - Program: | other | |||||||||
| HGF - Program Themes: | other | |||||||||
| DLR - Research area: | Digitalisation | |||||||||
| DLR - Program: | D - no assignment | |||||||||
| DLR - Research theme (Project): | D - EQUATE | |||||||||
| Location: | Köln-Porz | |||||||||
| Institutes and Institutions: | Institute for Software Technology | |||||||||
| Deposited By: | Epping, Michael | |||||||||
| Deposited On: | 14 Feb 2022 10:08 | |||||||||
| Last Modified: | 14 Feb 2022 10:08 |
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