Empirical Study of Observable Sets in Multiclass Quantum Classification
Paul San Sebastian, Mikel Cañizo, Roman Orus
TL;DR
This paper addresses native multiclass classification with parameterized quantum circuits by comparing two observable strategies: maximizing class-specific Pauli-string expectations and maximizing fidelity to class reference states via computational-basis projectors. It analyzes how observable locality drives Barren Plateaus and how observable structure influences Neural Collapse, using four datasets in noiseless simulations and two loss functions (cross-entropy and fidelity loss). The results show that projector-based observables can enforce an ETF-like structure on class means and promote Neural Collapse in low-dimensional settings, whereas non-commuting Pauli observables hinder ETF formation; in higher dimensions the curse of dimensionality blurs these differences. The work provides empirical guidance on observable design and reveals temperature regularization in softmax as a practical tool for improving generalization, suggesting avenues for future theory and model design in multiclass quantum learning.
Abstract
Variational quantum algorithms have gained attention as early applications of quantum computers for learning tasks. In the context of supervised learning, most of the works that tackle classification problems with parameterized quantum circuits constrain their scope to the setting of binary classification or perform multiclass classification via ensembles of binary classifiers (strategies such as one versus rest). Those few works that propose native multiclass models, however, do not justify the choice of observables that perform the classification. This work studies two main classification criteria in multiclass quantum machine learning: maximizing the expected value of an observable representing a class or maximizing the fidelity of the encoded quantum state with a reference state representing a class. To compare both approaches, sets of Pauli strings and sets of projectors into the computational basis are chosen as observables in the quantum machine learning models. Observing the empirical behavior of each model type, the effect of different observable set choices on the performance of quantum machine learning models is analyzed in the context of Barren Plateaus and Neural Collapse. The results provide insights that may guide the design of future multiclass quantum machine learning models.