Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Science and Technology

Trace-Distance Binary Tree AdaBoost for Trainable Quantum Multi-Class Classification

Xin Wang, Yabo Wang, Rebing Wu

Published Oct 23, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/2058-9565/aeb8f1

Related papers

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

Xin Wang, Yabo Wang, Rebing Wu

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.

quant-pharXiv:2602.02120•Feb 3, 2026•0 citations

Supervised-learning guarantee for quantum AdaBoost

Yabo Wang, Xin Wang, Bo Qi +1 more

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.

arXiv:2402.02376•Physical Review Applied•Nov 1, 2024•5 citations

Ensemble-learning error mitigation for variational quantum shallow-circuit classifiers

Qingyu Li, Yuhan Huang, Xiaokai Hou +3 more

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

arXiv:2301.12707•Physical Review Research•Jan 10, 2024•17 citations

Quantum ensemble learning with a programmable superconducting processor

Chao Song, Jiachen Chen, Yaozu Wu +30 more

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.

•Nov 25, 2024•0 citations

Quantum ensemble learning with a programmable superconducting processor

Jiachen Chen, Yaozu Wu, Zhen Yu Yang +30 more

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.

arXiv:2503.11047•npj Quantum Information•May 21, 2025•6 citations

Quantum embeddings for machine learning

Seth Lloyd, Maria Schuld, Aroosa Ijaz +2 more

Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional Hilbert space; the second part of the circuit executes a quantum measurement interpreted as the output of the model. Usually, the measurement is trained to distinguish quantum-embedded data. We propose to instead train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space, a strategy we call quantum metric learning. As a result, the measurement minimizing a linear classification loss is already known and depends on the metric used: for embeddings separating data using the l1 or trace distance, this is the Helstrom measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple overlap measurement. This approach provides a powerful analytic framework for quantum machine learning and eliminates a major component in current models, freeing up more precious resources to best leverage the capabilities of near-term quantum information processors.

arXiv:2001.03622•Jan 10, 2020•198 citations
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.
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.
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.
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 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.
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.
Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional Hilbert space; the second part of the circuit executes a quantum measurement interpreted as the output of the model. Usually, the measurement is trained to distinguish quantum-embedded data. We propose to instead train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space, a strategy we call quantum metric learning. As a result, the measurement minimizing a linear classification loss is already known and depends on the metric used: for embeddings separating data using the l1 or trace distance, this is the Helstrom measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple overlap measurement. This approach provides a powerful analytic framework for quantum machine learning and eliminates a major component in current models, freeing up more precious resources to best leverage the capabilities of near-term quantum information processors.