Quantum function fitting and classification beyond the single-qubit model

Abstract

Quantum Neural Networks (QNNs) have emerged as one promising Quantum Machine Learning (QML) technique. While the models for single and multi-qubit QNNs have been extensively studied, it remains unknown if using higher-dimensional systems provide any advantage. In this work, we investigate the theoretical foundation of the qubit model and we compare it with the qutrit prototype. First, we show that a single qubit can reproduce a Fourier series, while a qutrit can fit a more complicated type of function, with additional degrees of freedom that the model can adjust. Second, we explore the benefits of the third extra level of the qutrit for the classification task. In addition, we examine the two-qubit classifier and see that using a local cost function on the training improves the results, according to recent studies. Beyond the theoretical discussion, we provide numerical benchmarks of the models studied.