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arXiv:2602.02120

Towards Ultimate Accuracy in Quantum Multi-Class Classification: A Trace-Distance Binary Tree AdaBoost Classifier

Xin Wang, Yabo Wang, Rebing Wu

quant-phSubmitted Feb 2, 2026• Announced Feb 3, 2026• 0 citations
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Abstract

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.

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26 pages, 30 figures

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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.
Abstract 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 {heuristically} 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 almost 10,000 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.
In the noisy intermediate-scale quantum (NISQ) era, the capabilities of variational quantum algorithms are greatly constrained due to a limited number of qubits and the shallow depth of quantum circuits. We may view these variational quantum algorithms as weak learners in supervised learning. Ensemble methods are general approaches to combining weak learners to construct a strong one in machine learning. In this paper, by focusing on classification, we theoretically establish and numerically verify a learning guarantee for quantum adaptive boosting (AdaBoost). The supervised-learning risk bound describes how the prediction error of quantum AdaBoost on binary classification decreases as the number of boosting rounds and sample size increase. We further empirically demonstrate the advantages of quantum AdaBoost by focusing on a 4-class classification. The quantum AdaBoost not only outperforms several other ensemble methods, but in the presence of noise it can also surpass the ideally noiseless but unboosted primitive classifier after only a few boosting rounds. Our work indicates that in the current NISQ era, introducing appropriate ensemble methods is particularly valuable in improving the performance of quantum machine learning algorithms.
Quantum machine learning is among the most exciting potential applications of quantum computing. However, the vulnerability of quantum information to environmental noises and the consequent high cost for realizing fault tolerance has impeded the quantum models from learning complex datasets. Here, we introduce AdaBoost.Q, a quantum adaptation of the classical adaptive boosting (AdaBoost) algorithm designed to enhance learning capabilities of quantum classifiers. Based on the probabilistic nature of quantum measurement, the algorithm improves the prediction accuracy by refining the attention mechanism during the adaptive training and combination of quantum classifiers. We experimentally demonstrate the versatility of our approach on a programmable superconducting processor, where we observe notable performance enhancements across various quantum machine learning models, including quantum neural networks and quantum convolutional neural networks. With AdaBoost.Q, we achieve an accuracy above 86% for a ten-class classification task over 10,000 test samples, and an accuracy of 100% for a quantum feature recognition task over 1564 test samples. Our results demonstrate a foundational tool for advancing quantum machine learning towards practical applications, which has broad applicability to both the current noisy and the future fault-tolerant quantum devices.
Abstract Quantum machine learning is among the most exciting potential applications of quantum computing. However, the vulnerability of quantum information to environmental noises and the consequent high cost for realizing fault tolerance has impeded the quantum models from learning complex datasets. Here, we introduce Adaboost.Q, a quantum adaptation of the classical adaptive boosting (Adaboost) algorithm designed to enhance learning capabilities of quantum classifiers. Based on the probabilistic nature of quantum measurement, the algorithm improves the prediction accuracy by refining the attention mechanism during the adaptive training and combination of quantum classifiers. We experimentally demonstrate the versatility of our approach on a programmable superconducting processor, where we observe notable performance enhancements across various quantum machine learning models, including quantum neural networks and quantum convolutional neural networks. With Adaboost.Q, we achieve an accuracy above 86% for a ten-class classification task over 10,000 test samples, and an accuracy of 100% for a quantum feature recognition task over 1,564 test samples. Our results demonstrate a foundational tool for advancing quantum machine learning towards practical applications, which has broad applicability to both the current noisy and the future fault-tolerant quantum devices.
Classification is one of the main applications of supervised learning. Recent advancements in developing quantum computers have opened a new possibility for machine learning on such machines. Due to the noisy performance of near-term quantum computers, error mitigation techniques are essential for extracting meaningful data from noisy raw experimental measurements. Here, we propose two ensemble-learning error mitigation methods, namely, bootstrap aggregating and adaptive boosting, which can significantly enhance the performance of variational quantum classifiers for both classical and quantum datasets. The idea is to combine several weak classifiers, each implemented on a shallow noisy quantum circuit, to make a strong one with high accuracy. While both of our protocols substantially outperform error-mitigated primitive classifiers, the adaptive boosting shows better performance than the bootstrap aggregating. The protocols have been exemplified for classical handwriting digits as well as quantum phase discrimination of a symmetry-protected topological Hamiltonian, in which we observe a significant improvement in accuracy. Our ensemble-learning methods provide a systematic way of utilizing shallow circuits to solve complex classification problems. Published by the American Physical Society 2024
Abstract Hybrid quantum machine learning combines classical minimization with parameterized quantum circuits, enabling powerful learning models even on near-term quantum hardware. This work presents an evaluation of hybrid quantum machine learning classifiers using the data re-uploading framework across nine binary and multi-class classification tasks with varying geometric complexity. We compare three quantum circuit architectures, single-qubit, two-qubit, and two-qubit entangled, trained with three classical minimizers: COBYLA, Nelder-Mead, and SLSQP. Our experiments span training sizes from 1 to 200 samples and reveal that two-qubit classifiers, when paired with the SLSQP minimizer, achieve the highest overall test accuracy of 99.775% on structured tasks and strong performance (up to 89.78%) on complex multi-class pattern. Among minimizers, SLSQP consistently provides the best generalization, while entanglement improves accuracy in non-linear and fragmented tasks. By analyzing accuracy trends, generalization gaps, and confusion matrices, this study offers practical guidance for designing quantum classifiers that scale effectively and generalize well, providing a foundation for real-world Hybrid quantum machine learning applications.