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

TL;DR

The paper tackles the trainability bottlenecks of quantum multi-class classification by introducing the Trace-distance binary Tree AdaBoost (TTA) framework, which partitions classes through maximizing trace distance between average quantum states and trains binary AdaBoost ensembles of shallow PQCs at each node. By distributing learning across a trace-distance based binary tree and leveraging AdaBoost, TTA mitigates barren plateaus and quantum noise while maintaining strong generalization. Empirical evaluations on MNIST, synthetic datasets, and the ANNNI quantum phase diagram show 100% training accuracy and near-100% test accuracy, with about 0.2M total parameters and thousands of circuit layers distributed across many shallow models. The approach offers a practical, hardware-friendly path toward scalable quantum multi-class learning on near-term devices, supported by robustness analyses to noise and encoding choices and by open-source code.

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.

Figures (30)

• Figure 1: A schematic illustration of a trace-distance binary tree AdaBoost (TTA) multi-class classifier (a) Quantum state data of different classes and their average states. (b) Construction of a binary dataset tree by choosing splits that maximize the trace distance between the average states of two possible classes; each internal node holds a binary member classifier. (c) AdaBoost improves each member's train accuracy toward 100% and, together with QML generalization, yields near-perfect aggregate prediction. (d) Inference proceeds from the root to a leaf along node decisions to produce the final class label.
• Figure 2: Schematic illustration of a multi-class aggregate classifier constructed from an ensemble of binary AdaBoost member classifiers. Each member is an AdaBoost ensemble of binary quantum base classifiers: data are encoded or prepared as quantum states, evolved by a shallow parameterized circuit (layers of single-qubit $R_z$, $R_y$, and $R_z$ rotation gates plus ring-topology CNOT gates), and measured (Pauli-Z on the first qubit) to give binary outputs.
• Figure 3: Trace distance tree for the MNIST dataset. Each node is a binary member classifier, and red nodes indicate leaf nodes.
• Figure 4: Training and test accuracy comparison on the selected MNIST subset between the TTA classifier and other approaches, including single quantum multi-class classifier, quantum multi-class AdaBoost classifier, quantum bitwise aggregate classifier, as well as classical neural networks such as ResNet50 classifier and ViT small classifier. The TTA classifier achieves the best training and prediction performance compared to all other methods. The numbers on the error bars represent the average values of 5 runs, and the error bars represent the maximum and minimum values across the 5 runs.
• Figure 5: (a) Comparison of the number of base classifiers used by different quantum methods. (b) Parameter count comparison between the TTA classifier and classical neural networks. The numbers on the error bars represent the average values of 5 runs, and the error bars represent the maximum and minimum values.