Regression and Classification with Single-Qubit Quantum Neural Networks

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.