{
  "abstract": "Minimizing the number of CNOT gates required to synthesize a Clifford operator is a central problem in quantum circuit optimization. We extend the link--middle--cut (LMC) framework for linear reversible circuits to Clifford operators represented by binary symplectic tableaux. By introducing block-support connectivity graphs and determinantal invariants, we obtain efficiently computable lower bounds on ancilla-free CNOT complexity. We prove that these bounds are tight for qubit permutations: a permutation of $n$ qubits with $k$ cycles requires exactly $3(n-k)$ CNOT gates, even when arbitrary one-qubit Clifford gates are available. We also derive efficiently computable bounds for synthesis up to a permutation of the output qubits, corresponding to free qubit relabeling. Finally, we further demonstrate the utility of the bound by using it as an admissible heuristic for $A^*$-based Clifford synthesis and show that, on benchmark instances, the resulting search can prove optimality beyond what was possible with earlier SAT-based methods, and that it may be used in combination with earlier $A^*$ heuristics to improve the CNOT counts obtained through heuristic search.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16208",
  "author_total": 1,
  "authors": [
    {
      "name": "Søren Fuglede Jørgensen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0f7hxdfsbawhf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16208",
  "fulltext_url": null,
  "id": "0f7hxdfsbawhf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16208",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.16208",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0f7hxdfsbawhf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16208",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16208"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Link-middle-cut lower bounds for Clifford circuit synthesis",
  "title_text": "Link-middle-cut lower bounds for Clifford circuit synthesis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/0f7hxdfsbawhf",
  "venue": "arXiv",
  "versions": []
}