Empirical Study of Observable Sets in Multiclass Quantum Classification

2026-02-09

AI Summary

This work addresses the lack of systematic theoretical guidance in selecting observables for multi-class quantum classification. It presents the first empirical comparison between two dominant classification strategies—maximizing the expected value of class-specific observables and maximizing the fidelity between encoded states and reference states—and systematically evaluates the performance disparity between Pauli strings and computational-basis projection operators as observables. The study further investigates how these choices influence the emergence of Barren Plateaus and Neural Collapse phenomena. Experimental results based on variational quantum circuits demonstrate that the selection of observables significantly affects both training dynamics and final model performance, thereby offering critical empirical insights and actionable directions for designing and optimizing multi-class quantum machine learning architectures.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

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.

Problem

• multiclass quantum classification
• observable selection
• quantum machine learning
• Pauli strings
• computational basis projectors

Innovation

• multiclass quantum classification
• observable design
• Pauli strings
• fidelity-based classification
• Barren Plateaus