用单量子比特神经网络实现高效回归分类，训练速度远超传统方法。
Regression and Classification with Single-Qubit Quantum Neural Networks
- 采用参数化单量子比特门与测量实现资源高效学习。
- 分类任务可一步求解全局最优，训练速度显著提升。
- 在乳腺癌、MNIST等数据集上表现接近零误差，适合短期量子设备。
机器学习与量子计算相互促进，本文提出一种资源高效且可扩展的单量子比特量子神经网络（SQQNN），用于回归与分类任务。通过新型数据编码方式，SQQNN利用参数化单量子比特酉操作与量子测量实现高效学习。回归任务采用梯度下降法训练；分类任务引入受多项式回归启发的新训练方法，可在一步内高效求得变换后最小二乘目标的全局极小值，显著加速训练过程。在多个应用中评估显示，SQQNN在回归与分类任务中均表现出近乎零误差的优异性能，涵盖威斯康星乳腺癌与MNIST数据集。结果表明，SQQNN具备良好的泛化能力、可扩展性，适用于近中期量子设备部署。
原文摘要 · Abstract (English)
The literature reflects a mutually beneficial relationship between machine learning and quantum computing, where progress in one field frequently drives improvements in the other. Motivated by the rich connection between these areas, we use a resource-efficient and scalable Single-Qubit Quantum Neural Network (SQQNN) for both regression and classification tasks using a new data uploading technique. The SQQNN leverages parameterized single-qubit unitary operators and quantum measurements to achieve efficient learning. To train the model, we use gradient descent for regression tasks. For classification, we introduce a novel training method inspired by polynomial regression, which can efficiently find a global minimizer of the transformed least-squares objective in a single step. This approach significantly accelerates training compared to iterative methods. Evaluated across various applications, the SQQNN exhibits virtually error-free and strong performance in regression and classification tasks, including Wisconsin Breast Cancer and MNIST datasets. These results demonstrate the versatility, scalability, and suitability of the SQQNN for deployment on near-term quantum devices.
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