{
  "abstract": "Nonstabilizerness is a necessary resource for quantum systems to lie beyond the classically simulable regime. With the advent of stabilizer $α$-Rényi entropies, nonstabilizerness has also become a many-body diagnostic, complementary to entanglement. While deciding whether an arbitrary quantum state has nonstabilizerness is provably hard, such states already require a description exponentially large in the number of qubits and are thus out of reach for many-body physics. Here we instead consider 2D tensor network (TN) states, which compactly capture states obeying an entanglement area law, and ask whether they admit a simpler algorithm for the same task. In contrast to the 1D case, we prove that, even at small, constant bond dimension, computing the stabilizer entropy of 2D TN states is $\\#\\mathrm{P}$-hard for any integer $α\\ge 2$, and deciding stabilizer membership is $\\mathrm{C_=P}$-complete. The corresponding constant-accuracy problems remain $\\mathrm{C_= P}$-hard. We further prove that deciding whether a PEPS can be transformed into a stabilizer state by local unitaries over a specified bipartition is $\\mathrm{C_= P}$-hard. Under standard complexity assumptions, these results rule out classical or quantum algorithms with polynomial resources for all three tasks in the worst case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31459",
  "author_total": 2,
  "authors": [
    {
      "name": "Gianluca Esposito"
    },
    {
      "name": "Georgios Styliaris"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5y9znszmdwy2m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31459",
  "fulltext_url": null,
  "id": "5y9znszmdwy2m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31459",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7214571756",
  "pdf_url": "https://arxiv.org/pdf/2609.31459",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5y9znszmdwy2m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.31459",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31459"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Nonstabilizerness of quantum tensor network states is intractable in two dimensions",
  "title_text": "Nonstabilizerness of quantum tensor network states is intractable in two dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/5y9znszmdwy2m",
  "venue": "arXiv",
  "versions": []
}