Empirical Study of Observable Sets in Multiclass Quantum Classification

TL;DR

This paper empirically compares two classification criteria in multiclass quantum machine learning, analyzing how different observable sets influence model performance and providing insights for future model design.

Contribution

It investigates the impact of observable set choices on multiclass quantum classifiers, addressing a gap in understanding of native quantum multiclass models.

Findings

Observable set choice affects model performance.

Fidelity-based observables show different behavior than expectation value-based.

Insights inform future design of quantum multiclass classifiers.

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.