{
  "abstract": "Consider the following optimization problem over stabilizer product states: given an $n$-qubit stabilizer state $\\left|ψ\\right\\rangle$ and a set of single-qubit stabilizer states $S$, maximize $\\left|\\langle ψ| ϕ_1, \\ldots, ϕ_n \\rangle\\right|^2$ over single-qubit stabilizer states $\\left|ϕ_i\\right\\rangle \\in S$. By varying the set $S$, we show that solutions to this problem can be useful in a variety of settings: tighter runtime bounds for certain classical simulation algorithms; measures of entanglement; and the complexity of low-rank matrix completion. Moreover, we give a complete complexity classification of this nearest stabilizer product state problem. After accounting for the symmetries in the Clifford group, there are $9$ distinct possible sets $S$, and we show that all but the two simplest of these are $\\NP$-complete.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02037",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniel Grier"
    },
    {
      "name": "Hakop Pashayan"
    },
    {
      "name": "Luke Schaeffer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/be33198dzyvhb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02037",
  "fulltext_url": null,
  "id": "be33198dzyvhb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02037",
  "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": "W7216587300",
  "pdf_url": "https://arxiv.org/pdf/2610.02037",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/be33198dzyvhb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02037",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02037"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Complexity and Applications of Nearest Stabilizer Product State Problems",
  "title_text": "Complexity and Applications of Nearest Stabilizer Product State Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/be33198dzyvhb",
  "venue": "arXiv",
  "versions": []
}