Quantum Computing offers a new paradigm for efficient computing and many AI applications could benefit from its potential boost in performance. However, the main limitation is the constraint to linear operations that hampers the representation of complex relationships in data. In this work, we propose an efficient implementation of quantum splines for non-linear approximation. In particular, we first discuss possible parametrisations, and select the most convenient for exploiting the HHL algorithm to obtain the estimates of spline coefficients. Then, we investigate QSpline performance as an evaluation routine for some of the most popular activation functions adopted in ML. Finally, a detailed comparison with classical alternatives to the HHL is also presented.

翻译：量子计算为高效计算提供了新范式，许多人工智能应用可能受益于其潜在的性能提升。然而，其主要限制在于线性运算约束，这阻碍了数据中复杂关系的表示。在本工作中，我们提出了一种用于非线性近似的量子样条高效实现方案。具体而言，我们首先讨论了可能的参数化方法，并选择最有利于利用HHL算法获取样条系数估计的方案。随后，我们研究了QSpline作为评估例程在机器学习中最常用的若干激活函数上的性能表现。最后，我们还与经典替代HHL算法的方法进行了详细比较。