A Quantum Photonic Approach to Graph Coloring

Quantum Physics arXiv:2601.20263 (quant-ph) [Submitted on 28 Jan 2026] Title:A Quantum Photonic Approach to Graph Coloring Authors:Jesua Epequin, Pascale Bendotti, Joseph Mikael View a PDF of the paper titled A Quantum Photonic Approach to Graph Coloring, by Jesua Epequin and 2 other authors View PDF HTML (experimental) Abstract:Gaussian Boson Sampling (GBS) is a quantum computational model that leverages linear optics to solve sampling problems believed to be classically intractable. Recent experimental breakthroughs have demonstrated quantum advantage using GBS, motivating its application to real-world combinatorial optimization problems. In this work, we reformulate the graph coloring problem as an integer programming problem using the independent set formulation. This enables the use of GBS to identify cliques in the complement graph, which correspond to independent sets in the original graph. Our method is benchmarked against classical heuristics and exact algorithms on two sets of instances: Erdős-Rényi random graphs and graphs derived from a smart-charging use case. The results demonstrate that GBS can provide competitive solutions, highlighting its potential as a quantum-enhanced heuristic for graph-based optimization. Comments: Subjects: Quantum Physics (quant-ph); Discrete Mathematics (cs.DM) Cite as: arXiv:2601.20263 [quant-ph] (or arXiv:2601.20263v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.20263 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jesua Israel Epequin Chavez [view email] [v1] Wed, 28 Jan 2026 05:18:27 UTC (2,072 KB) Full-text links: Access Paper: View a PDF of the paper titled A Quantum Photonic Approach to Graph Coloring, by Jesua Epequin and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cs cs.DM References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)