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.

翻译：由于经典机器学习已成为开发数据驱动算法的强大工具，量子机器学习有望对量子算法的发展产生类似影响。现有文献反映了机器学习与量子计算之间互利共生的关系，其中一个领域的进展常常推动另一领域的改进。受参数化量子电路所实现的机器学习与量子计算之间富有成效的联系启发，我们采用一种资源高效且可扩展的单量子比特量子神经网络（SQQNN）同时处理回归与分类任务。SQQNN利用参数化单量子比特酉算符与量子测量来实现高效学习。对于回归任务，我们采用梯度下降法训练模型。针对分类任务，我们提出一种受泰勒级数启发的新型训练方法，该方法能在单步内高效找到全局最小值。相较于迭代方法，此方法显著加速了训练过程。经多种应用场景评估，SQQNN在回归与分类任务（包括MNIST数据集）中表现出近乎无误差的优异性能。这些结果证明了SQQNN的通用性、可扩展性及其在近期量子设备上部署的适用性。