{
  "abstract": "$\\mathsf{QAC}^0$ is the class of constant-depth $\\mathrm{poly}(n)$-ancilla circuits obtained by extending $\\mathsf{QNC}^0$, the class of local circuits, to include nonlocal interactions via arbitrary width Toffoli gates. It is believed to be weaker than its counterpart, $\\mathsf{QNC}^0_f$, obtained by including arbitrary-width FANOUT gates instead ($\\mathsf{QAC}^0 \\subseteq \\mathsf{QNC}^0_f$ [Moo99]). In this note, we show that every $O(\\log n)$-qubit state can be exactly and cleanly prepared by a $\\mathrm{poly}(n)$-ancilla $\\mathsf{QAC}^0$ circuit. Previous known $\\mathrm{poly}(n)$-ancilla circuits for arbitrary such states are only known via additional access to either FANOUT or QRAM (indexing) gates [Ros21b, GGJ26b], neither of which are known to be in $\\mathsf{QAC}^0$. Equivalently, prior constructions of arbitrary $n$-qubit states in $\\mathsf{QAC}^0$ require doubly exponential size and we obtain an exponential factor improvement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17408",
  "author_total": 3,
  "authors": [
    {
      "name": "Lucas Gretta"
    },
    {
      "name": "Meghal Gupta"
    },
    {
      "name": "Malvika Raj Joshi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8cqgq9hdw2d44.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17408",
  "fulltext_url": null,
  "id": "8cqgq9hdw2d44",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17408",
  "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",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213429256",
  "pdf_url": "https://arxiv.org/pdf/2609.17408",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8cqgq9hdw2d44.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.17408",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17408"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "QAC0 Can Prepare Every Logarithmic-Qubit State",
  "title_text": "QAC0 Can Prepare Every Logarithmic-Qubit State",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/8cqgq9hdw2d44",
  "venue": "arXiv",
  "versions": []
}