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PreprintCC BY 4.0arXiv

From hyperplanes to hyperellipsoids: a pedagogical bridge from linear classifiers to single-qubit mixed-state classifiers

  • Kaitlin Gili
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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.

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Cite

BibTeXRIS
BibTeX
@misc{gili2026from,
  title = {{From hyperplanes to hyperellipsoids: a pedagogical bridge from linear classifiers to single-qubit mixed-state classifiers}},
  author = {Kaitlin Gili},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.15433},
  eprint = {2607.15433},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.15433},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - From hyperplanes to hyperellipsoids: a pedagogical bridge from linear classifiers to single-qubit mixed-state classifiers
AU  - Kaitlin Gili
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2607.15433
UR  - https://arxiv.org/abs/2607.15433
AB  - 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.
ER  -