Empirical Study of Observable Sets in Multiclass Quantum Classification
This work addresses a gap in quantum machine learning for multiclass classification, offering empirical guidance on observable selection, but it is incremental as it builds on existing variational quantum algorithms without introducing a new paradigm.
The paper tackled the lack of justification for observable choices in native multiclass quantum classification models by empirically comparing two classification criteria—maximizing expected values of observables and maximizing fidelity with reference states—using sets of Pauli strings and projectors. The results analyzed the effects on performance in contexts like Barren Plateaus and Neural Collapse, providing insights for future model design.
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.