# Empirical Study of Observable Sets in Multiclass Quantum Classification

arXiv: https://arxiv.org/abs/2602.08485 · HTML: https://mlsanity.com/paper/2602.08485/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 64 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 27 of 27)

- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Neural collapse with unconstrained features](https://mlsanity.com/paper/2011.11619/) (2020)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [An Unconstrained Layer-Peeled Perspective on Neural Collapse](https://mlsanity.com/paper/2110.02796/) (2021)
- [Imbalance Trouble: Revisiting Neural-Collapse Geometry](https://mlsanity.com/paper/2208.05512/) (2022)
- [A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning](https://mlsanity.com/paper/2109.02355/) (2021)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [On barren plateaus and cost function locality in variational quantum algorithms](https://mlsanity.com/paper/2011.10530/) (2020)
- [Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification](https://mlsanity.com/paper/2301.01597/) (2022)
- [Quantum Machine Learning: A Hands-on Tutorial for Machine Learning Practitioners and Researchers](https://mlsanity.com/paper/2502.01146/) (2025)
- [QUILT: Effective Multi-Class Classification on Quantum Computers Using an Ensemble of Diverse Quantum Classifiers](https://mlsanity.com/paper/2309.15056/) (2023)
- [Quantifying the Variability Collapse of Neural Networks](https://mlsanity.com/paper/2306.03440/) (2023)
- [An All-Pair Quantum SVM Approach for Big Data Multiclass Classification](https://mlsanity.com/paper/1704.07664/) (2017)
- [Projection Valued Measure-based Quantum Machine Learning for Multi-Class Classification](https://mlsanity.com/paper/2210.16731/) (2022)
- [Leveraging Intermediate Neural Collapse with Simplex ETFs for Efficient Deep Neural Networks](https://mlsanity.com/paper/2412.00884/) (2024)

## Abstract (arXiv)

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.