# Regression and Classification with Single-Qubit Quantum Neural Networks

arXiv: https://arxiv.org/abs/2412.09486 · HTML: https://mlsanity.com/paper/2412.09486/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 12 of 12)

- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [The Principles of Deep Learning Theory](https://mlsanity.com/paper/2106.10165/) (2021)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Towards provably efficient quantum algorithms for large-scale machine-learning models](https://mlsanity.com/paper/2303.03428/) (2023)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [Quantum Perceptron Models](https://mlsanity.com/paper/1602.04799/) (2016)
- [Power and limitations of single-qubit native quantum neural networks](https://mlsanity.com/paper/2205.07848/) (2022)
- [Simulating a perceptron on a quantum computer](https://mlsanity.com/paper/1412.3635/) (2014)
- [Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning](https://mlsanity.com/paper/2203.15368/) (2022)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Quantum perceptron over a field and neural network architecture selection in a quantum computer](https://mlsanity.com/paper/1602.00709/) (2016)

## Built on by (most cited first, 2 of 2)

- [Single-Qudit Quantum Neural Networks for Multiclass Classification](https://mlsanity.com/paper/2503.09269/) (2025)
- [Supervised Quantum Machine Learning: A Future Outlook from Qubits to Enterprise Applications](https://mlsanity.com/paper/2505.24765/) (2025)

## Abstract (arXiv)

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.