{
  "abstract": "Montanaro and Zhou proved that depth-one Quantum Approximate Optimization Algorithm (QAOA) finds the planted solution of certain near-symmetric constraint satisfaction problems with probability $Ω(1)$, and observed exponential runtimes for general-purpose classical solvers on explicit realizations, providing strong evidence of an empirical exponential speedup of low-depth QAOA. We ask what such a circuit costs fault-tolerantly. Although the cost Hamiltonian carries $Θ(n^\\ell)$ clauses, the rotation angle at which QAOA succeeds shrinks as $n^{1-\\ell}$, and we show that small-angle Clifford$+T$ rotation synthesis reduces the non-Clifford cost per circuit to $\\widetilde O(n^2)$ for every clause locality $\\ell$. Compiling the circuit, however, requires the explicit clause list. We find that the mechanism underlying constant QAOA success fixes the degree-one Fourier coefficients of the cost, whose signs reveal the planted solution. However, this leakage need not reveal the solution: we design families in which the quadratic non-Clifford scaling and hard exact optimization coexist.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39922",
  "author_total": 3,
  "authors": [
    {
      "name": "Jernej Rudi Finžgar"
    },
    {
      "name": "Martin Leib"
    },
    {
      "name": "Elisabeth Wybo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/00dwj8d3pxprj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39922",
  "fulltext_url": null,
  "id": "00dwj8d3pxprj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39922",
  "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": "W7215053603",
  "pdf_url": "https://arxiv.org/pdf/2609.39922",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/00dwj8d3pxprj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39922",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39922"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fault-tolerant cost of shallow QAOA on near-symmetric optimization problems",
  "title_text": "Fault-tolerant cost of shallow QAOA on near-symmetric optimization problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/00dwj8d3pxprj",
  "venue": "arXiv",
  "versions": []
}