标题： 带有单量子比特量子神经网络的回归与分类 显示英文标题

标题： Regression and Classification with Single-Qubit Quantum Neural Networks

摘要： 自从经典机器学习已成为开发数据驱动算法的强大工具，量子机器学习预计也将对量子算法的发展产生类似的影响。 文献反映了机器学习和量子计算之间的互利关系，其中一个领域的进步经常推动另一个领域的改进。 受参数化量子电路所促成的机器学习与量子计算之间丰富联系的启发，我们使用一种资源高效且可扩展的单量子比特量子神经网络（SQQNN）来进行回归和分类任务。 SQQNN利用参数化的单量子比特酉算子和量子测量来实现高效的学习。 为了训练模型，我们使用梯度下降法进行回归任务。 对于分类任务，我们引入了一种受泰勒级数启发的新训练方法，该方法可以高效地在一步中找到全局最小值。 与迭代方法相比，这种方法显著加快了训练速度。 在各种应用中进行评估，SQQNN在回归和分类任务中表现出几乎无误差且强大的性能，包括MNIST数据集。 这些结果展示了SQQNN的多功能性、可扩展性和适用于近期量子设备部署的适用性。 显示英文摘要

摘要： Since classical machine learning has become a powerful tool for developing data-driven algorithms, quantum machine learning is expected to similarly impact the development of quantum algorithms. 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 fertile connection between machine learning and quantum computing enabled by parameterized quantum circuits, we use a resource-efficient and scalable Single-Qubit Quantum Neural Network (SQQNN) for both regression and classification tasks. 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 the Taylor series, which can efficiently find a global minimum 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 the MNIST dataset. These results demonstrate the versatility, scalability, and suitability of the SQQNN for deployment on near-term quantum devices.