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

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.