Variational Quantum Regression on NISQ Hardware with Error Mitigation

At the intersection of two promising technologies, Machine Learning (ML) and Quantum Computing (QC), Quantum Machine Learning (QML) emerges. However, while QC is still in an early stage of development, QML is even more so. In this study, the Auto-MPG dataset was selected for its dimension, making it suitable for QML tasks within the current limitations of quantum hardware, especially regarding qubit requirements. Unlike classification problems that dominate the literature, regression problems have only been explored theoretically. This study aims to bridge that gap by applying QML techniques to a practical regression task. To this end, a preliminary analysis was conducted using a classical model as a reference point for subsequent evaluation. The quantum experimentation was performed in two phases: first, the model was trained in an ideal simulator to determine the model's best hyperparameters. Then, these best models were run in a noisy simulator using quantum error mitigation techniques. The results show how the Variational Quantum Algorithms (VQA) outperforms classical Extreme Gradient Boosting and the methods used to mitigate errors in quantum hardware are effective, as they achieve comparable results between the noisy simulator and the perfect simulator. This brings closer the possible applications in NISQ current devices.