Quantum splines for non-linear approximations

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.