The development of quantum neural networks (QNNs) has attracted considerable attention due to their potential to surpass classical models in certain machine learning tasks. Nonetheless, it remains unclear under which conditions QNNs provide concrete benefits over classical neural networks (CNNs). This study addresses this question by performing both qualitative and quantitative analyses of classical and quantum models applied to regression problems, using two target functions with contrasting properties. Additionally, the work explores the methodological difficulties inherent in making fair comparisons between QNNs and CNNs. The findings reveal a distinct advantage of QNNs in a specific quantum machine learning context. In particular, QNNs excelled at approximating the sinusoidal function, achieving errors up to seven orders of magnitude lower than their classical counterparts. However, their performance was limited in other cases, emphasizing that QNNs are highly effective for certain tasks but not universally superior. These results reinforce the principles of the “No Free Lunch” theorem, highlighting that no single model outperforms all others across every problem domain.
Lima et al. (Tue,) studied this question.