{
  "abstract": "We study the problem of tomography for $k$-sparse quantum states. In contrast to classical distribution learning, where tight sample and time complexity bounds in terms of support size are well understood, no non-trivial bounds were previously shown for this problem. We give the first near optimal algorithm for learning $n$-qubit $k$-sparse pure quantum states, obtaining fidelity at least $1-\\varepsilon$ with high probability using $\\tilde{O}(k/\\varepsilon)$ copies of the state and $\\tilde{O}(kn/\\varepsilon)$ time. Both bounds are optimal up to polylogarithmic factors. As an implication, we also obtain an algorithm with near optimal $\\tilde{O}(kr/\\varepsilon)$ sample complexity for learning $k$-sparse rank-$r$ mixed states, via the random purification channel technique. Obtaining time complexity nearly matching the sample complexity, for $r>1$, remains an important open question.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12219",
  "author_total": 1,
  "authors": [
    {
      "name": "Aniruddha Sen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3c6qzchfx6g7g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12219",
  "fulltext_url": null,
  "id": "3c6qzchfx6g7g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12219",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212753344",
  "pdf_url": "https://arxiv.org/pdf/2609.12219",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3c6qzchfx6g7g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12219",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12219"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Learning Sparse Quantum States",
  "title_text": "Learning Sparse Quantum States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:07Z",
  "url": "https://research.draconitic.com/paper/3c6qzchfx6g7g",
  "venue": "arXiv",
  "versions": []
}