{
  "abstract": "Graph coloring is a well-known NP-complete problem with applications in scheduling, register allocation, frequency assignment, and network optimization. Quantum computing offers the potential for polynomial or even super-polynomial speedups in certain problem instances, yet practical quantum graph coloring methods must carefully balance qubit resources, circuit depth, and constraint enforcement. We proposed a solver agnostic quantum framework for $K$-coloring. Along with a novel encoding and efficient constraint implementation for its exact coloring exploiting Grover search and almost optimal coloring by the Quantum Approximate Optimization Algorithm \\emph{(QAOA)}, and \\emph{Quantum Annealing}. Unlike using $O(NK)$ qubits as in \\emph{SOTA}, we reduced the qubit requirements to $O(N \\log_2 K)$, along with optimized comparator circuits enforcing adjacency constraints. Further symmetry-based graph reduction is incorporated as an optional preprocessing step to further reduce the instance size before quantum execution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32348",
  "author_total": 2,
  "authors": [
    {
      "name": "Lord Sen"
    },
    {
      "name": "Shyamapada Mukherjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21c43degjj3ja.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32348",
  "fulltext_url": null,
  "id": "21c43degjj3ja",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32348",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.32348",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/21c43degjj3ja.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.32348",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32348"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Quantum Framework for K Coloring of Graphs",
  "title_text": "A Quantum Framework for K Coloring of Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/21c43degjj3ja",
  "venue": "arXiv",
  "versions": []
}