{
  "abstract": "Temporary occupation of qutrit levels can reduce the width and depth required for binary circuit logic in quantum computing. We introduce an efficient intermediate-qutrit decomposition of multi-controlled Toffoli gates with binary-subspace inputs and outputs. For balanced control widths $n=2^h-1$, the proposed decomposition is evaluated hierarchically through a tree, allowing independent subtree computations to proceed in parallel and reducing the depth from linear to logarithmic. The balanced low-depth construction requires $6n+3$ logical $P_9$ injections and $\\frac{n-3}{4}$ clean ancillary qutrits. It matches the direct $P_9$ count of a recursively extended Clifford+$P_9$ baseline derived from the state-of-the-art work while using asymptotically one-quarter as many clean ancillas and replacing linear depth with logarithmic depth. For arbitrary control widths, a sequential extension preserves the $6n+3$ $P_9$ count but has depth $O(\\log m+n-m)$ for a balanced core $m=2^h-1\\leq n$, which is linear in the worst case over $n$. By reducing the resource overhead of a widely used reversible primitive, the proposed decomposition provides a practical building block for the design and compilation of more resource-efficient quantum algorithms in the fault-tolerant regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29884",
  "author_total": 2,
  "authors": [
    {
      "name": "Amit Saha"
    },
    {
      "name": "Francesco Arzani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4xy8e09x9fa5j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29884",
  "fulltext_url": null,
  "id": "4xy8e09x9fa5j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29884",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214300777",
  "pdf_url": "https://arxiv.org/pdf/2609.29884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4xy8e09x9fa5j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29884"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient Synthesis of Multi-Controlled Toffoli Gates with Ternary Clifford$+P_9$ Gates",
  "title_text": "Efficient Synthesis of Multi-Controlled Toffoli Gates with Ternary Clifford+P_9 Gates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/4xy8e09x9fa5j",
  "venue": "arXiv",
  "versions": []
}