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: rath...

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