{
  "abstract": "In this work we study the robustness of $\\mathsf{QAC}^0$ with respect to error tolerance and modifications to its gate-set. First, we investigate whether the non-zero error typically allowed for $\\mathsf{QAC}^0$ circuits computing Boolean functions is truly necessary. We show that the error inherent in the parallel $W$-test of \\cite{grier_morris_wu} can be eliminated entirely via a novel application of exact amplitude amplification in the many-copies context. Consequently, we find that $\\mathsf{QAC}^0$ can \\textit{exactly} simulate $\\mathsf{TC}^0$ with polynomially many copies of the classical input and that for every fixed prime $p$ exact $\\mathsf{QAC}^0$, $\\mathsf{EQAC}^0$, can compute total Boolean functions outside of $\\mathsf{AC}^0[p]$. Second, we ask to what extent the computational power of $\\mathsf{QAC}^0$ follows from the fact that arbitrary single-qubit gates may be used at any point in the circuit. We find that $\\mathsf{QAC}^0$ is in fact robust to restrictions on which single-qubit gates are permitted: every $\\mathsf{QAC}^0$ circuit can be approximately implemented by a $\\mathsf{QAC}^0$ circuit consisting of just generalized Toffoli, $S$, and Hadamard gates. Moreover, this approximating circuit can be constructed efficiently from a classical description of the original circuit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02154",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniel Grier"
    },
    {
      "name": "Jackson Morris"
    },
    {
      "name": "Kewen Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7eq5v24s80k5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02154",
  "fulltext_url": null,
  "id": "7eq5v24s80k5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02154",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7216403644",
  "pdf_url": "https://arxiv.org/pdf/2610.02154",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7eq5v24s80k5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02154",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02154"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Robustness of QAC0",
  "title_text": "The Robustness of QAC0",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/7eq5v24s80k5g",
  "venue": "arXiv",
  "versions": []
}