{
  "abstract": "Highly entangled and highly non-stabilizer quantum states need not be hard to learn. We give efficient algorithms for testing and recovering hidden tensor-product structure in unknown pure state vectors of the form $\\lvertψ\\rangle = U_C \\bigotimes_i \\lvertψ_i\\rangle$, where $U_C$ is an arbitrary unknown Clifford unitary. Although the Clifford can thoroughly scramble the visible product structure, we prove that the Bell distribution retains a characteristic family of quadratic symmetries. By simultaneously block-diagonalising these symmetries, our algorithms linearize the problem and manage to recover both a disentangling Clifford and the hidden partitions with polynomial sample and computational complexity. This may be viewed as an extension of the abelian StateHSP paradigm in which classical post-processing exposes genuinely quadratic structure. Applied to Choi states, the method yields efficient proper learning algorithms for typical $t$-doped Clifford unitaries in regimes containing exponentially more $T$ gates than previously accessible: the required condition fails only for an exponentially small fraction of circuits when $t\\sim n$, and continues to hold for a constant fraction even when $t=2n$. Our framework also provides tools for compressing structured many-body Hamiltonians and suggests benchmarking protocols for encoded logical product states in the early fault-tolerant regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27565",
  "author_total": 4,
  "authors": [
    {
      "name": "Gerard Aguilar"
    },
    {
      "name": "Sofiene Jerbi"
    },
    {
      "name": "Jens Eisert"
    },
    {
      "name": "Lennart Bittel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cz2pnc6mv9p69.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27565",
  "fulltext_url": null,
  "id": "cz2pnc6mv9p69",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27565",
  "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": "W7214191848",
  "pdf_url": "https://arxiv.org/pdf/2609.27565",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cz2pnc6mv9p69.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27565",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27565"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient learning of Clifford disentanglers and typical $t$-doped unitaries with exponentially more $T$ gates",
  "title_text": "Efficient learning of Clifford disentanglers and typical t-doped unitaries with exponentially more T gates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/cz2pnc6mv9p69",
  "venue": "arXiv",
  "versions": []
}