From hyperplanes to hyperellipsoids: characterizing the inherent interpretability of linear and single-qubit mixed-state binary classification models
This paper characterizes and compares the inherent interpretability of standard linear models and single-qubit mixed-state models for binary classification. It finds that the single-qubit model learns a hyperellipsoid instead of a hyperplane, making it the "ellipsoid version" of linear classification. The authors discuss the geometric and feature importance inductive biases of both models, offering an accessible introduction to quantum ML for readers with only linear classification knowledge.
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[Submitted on 16 Jul 2026]
Title:From hyperplanes to hyperellipsoids: characterizing the inherent interpretability of linear and single-qubit mixed-state binary classification models
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Abstract:We characterize and compare the inherent interpretability offerings of a standard linear model with a single qubit mixed state model for the task of supervised binary classification. A side by side comparison reveals that a single qubit mixed state model for binary classification is just the ``ellipsoid version" of standard linear model classification. More precisely, rather than learning a hyperplane to classify data, we learn a hyperellipsoid. We discuss the consequences of the geometric inductive biases of both models, as well as how each model contains a different feature importance inductive bias. This short characterization offers an accessible route to quantum machine learning (ML) ideas for readers who have zero background in quantum and are only familiar with linear classification in ML. In support of ML pedagogy, we encourage instructors to utilize this piece to smoothly introduce quantum ML ideas into the undergraduate ML classroom.
Subjects:
Machine Learning (cs.LG); Quantum Physics (quant-ph)
Cite as: arXiv:2607.15433 [cs.LG]
(or arXiv:2607.15433v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.15433
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Kaitlin Gili [view email] [v1] Thu, 16 Jul 2026 20:07:35 UTC (700 KB)
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