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arXiv:2604.08094

Divide et impera: hybrid multinomial classifiers from quantum binary models

Simone Roncallo, Angela Rosy Morgillo, Seth Lloyd, Chiara Macchiavello, Lorenzo Maccone

quant-phSubmitted Apr 9, 2026• Announced Apr 10, 2026• 0 citations
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Abstract

We investigate how to combine a collection of quantum binary models into a multinomial classifier. We employ a hybrid approach, adopting strategies like one-vs-one, one-vs-rest and a binary decision tree. We benchmark each method, by emphasizing their computational overhead and their impact on the quantum advantage. By comparison against a classical binary model (generalized using the same approach), we show that the decision tree represents a cost-effective solution, achieving similar accuracies to other methods with an overhead at most logarithmic in the total number of classes.

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5 pages, 1 figure;

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We investigate how to combine a collection of quantum binary models into a multinomial classifier. We employ a hybrid approach, adopting strategies like one-vs-one, one-vs-rest and a binary decision tree. We benchmark each method, by emphasizing their computational overhead and their impact on the quantum advantage. By comparison against a classical binary model (generalized using the same approach), we show that the decision tree represents a cost-effective solution, achieving similar accuracies to other methods with an overhead at most logarithmic in the total number of classes.
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We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision tree can be realized via measurements of a quantum circuit. We describe how tree inductions and the prediction of class labels of query data can be integrated into this framework. An on-demand sampling method enables predictions with a constant number of classical memory slots, independent of the tree depth. We experimentally study our approach using both a quantum computing simulator and actual IBM quantum hardware. To our knowledge, this is the first realization of a decision tree classifier on a quantum device.
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We propose a Trace-distance binary Tree AdaBoost (TTA) multi-class quantum classifier, a practical pipeline for quantum multi-class classification that combines quantum-aware reductions with ensemble learning to improve trainability and resource efficiency. TTA builds a hierarchical binary tree by choosing, at each internal node, the bipartition that maximizes the trace distance between average quantum states; each node trains a binary AdaBoost ensemble of shallow variational quantum base learners. By confining intrinsically hard, small trace distance distinctions to small node-specific datasets and combining weak shallow learners via AdaBoost, TTA distributes capacity across many small submodels rather than one deep circuit, mitigating barren-plateau and optimization failures without sacrificing generalization. Empirically TTA achieves top test accuracy ($\approx $100\%) among quantum and classical baselines, is robust to common quantum errors, and realizes aggregate systems with 10000 cumulative layers and 0.2M parameters, implemented as many shallow circuits. Our results are empirical and implementable on near-term platforms, providing a resource-efficient route to scalable multi-class quantum machine learning.