标题： 评估量子神经网络在回归任务中的优势和局限性 显示英文标题

标题： Assessing the Advantages and Limitations of Quantum Neural Networks in Regression Tasks

摘要： 量子神经网络（QNNs）的发展由于其在某些机器学习任务中可能超越经典模型的潜力而引起了广泛关注。 然而，尚不清楚在何种条件下QNNs能比经典神经网络（CNNs）提供具体的优点。 本研究通过定性和定量分析，对回归问题中应用的经典和量子模型进行了研究，使用了两个具有对比特性的目标函数。 此外，该工作探讨了在QNNs和CNNs之间进行公平比较时固有的方法论困难。 研究结果揭示了在特定量子机器学习情境下QNNs的优势。 特别是，QNNs在近似正弦函数方面表现出色，其误差比经典模型低多达七个数量级。 然而，在其他情况下，它们的性能受到限制，强调了QNNs对于某些任务非常有效，但并非普遍优于所有情况。 这些结果强化了“没有免费午餐”定理的原则，突显了没有一个模型能在所有问题领域中都优于其他模型。 显示英文摘要

摘要： 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 sPuperior. These results reinforce the principles of the ``No Free Lunch'' theorem, highlighting that no single model outperforms all others across every problem domain.