{
  "abstract": "Quantum machine learning ideas are typically absent from traditional machine learning curricula and are instead introduced in upper-level courses on quantum information processing and quantum computing. We propose a route for bringing quantum ideas into the standard machine learning classroom directly after the introduction of binary linear classifiers. Specifically, we develop a pedagogical bridge between linear classifiers and single-qubit mixed-state classifiers by characterizing their geometric model structure. This characterization reveals that a single-qubit mixed-state model for binary classification can be viewed as the ``ellipsoidal version'' of a standard linear classifier: rather than learning a hyperplane that separates data, the model learns a hyperellipsoid.. We present this connection as an accessible bridge from familiar classical machine learning concepts to quantum machine learning, and encourage instructors to use it as a natural entry point for introducing quantum ideas in the undergraduate machine learning classroom.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.15433",
  "author_total": 1,
  "authors": [
    {
      "name": "Kaitlin Gili"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4j0qsrv2c5b4r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.15433",
  "fulltext_url": null,
  "id": "4j0qsrv2c5b4r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.15433",
  "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.LG"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7169788704",
  "pdf_url": "https://arxiv.org/pdf/2607.15433",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4j0qsrv2c5b4r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2607.15433",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.15433"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "From hyperplanes to hyperellipsoids: a pedagogical bridge from linear classifiers to single-qubit mixed-state classifiers",
  "title_text": "From hyperplanes to hyperellipsoids: a pedagogical bridge from linear classifiers to single-qubit mixed-state classifiers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:11Z",
  "url": "https://research.draconitic.com/paper/4j0qsrv2c5b4r",
  "venue": "arXiv",
  "versions": []
}