M-band Wavelet Kernels for Classical and Quantum SVM

In this research, brand-new M-Band Wavelet Kernels within both classical and quantum environments are constructed for corresponding Support Vector Machines (SVM). Unlike kernels such as Gaussian RBF, our wavelet kernels in the classical case map the input space into a finite dimensional feature space of dimension 0(K^N), where K is the M-Band Wavelet compact support constant and N is the dimension of the input space. However, the kernel expression is simplified under quantum environment so that the quantum wavelet kernel will map the same input space to the feature space of dimension 0(K) only. Moreover, it is assumed there are P training points, then the complexity upon the training data comes to 0(Nlog P). Compared with the classical method of complexity being 0(P²K^N), there is an exponential speedup.