  Quantum algorithms based on quantum kernel methods have been investigated
previously [1]. A quantum advantage is derived from the fact that it is
possible to construct a family of datasets for which, only quantum processing
can recognise the intrinsic labelling patterns, while for classical computers
the dataset looks like noise. This is due to the algorithm leveraging inherent
efficiencies in the computation of logarithms in a cyclic group. The discrete
log problem.is a well-known advantage of quantum vs classical computation:
where it is possible to generate all the members of the group using a single
mathematical operation. Kernel methods are a powerful and popular technique in
classical Machine Learning. The use of a quantum feature space that can only be
calculated efficiently on a quantum computer potentially allows for deriving a
quantum advantage. In this paper, we intend to first describe the application
of such a kernel method to a Quantum version of the classical Support Vector
Machine (SVM) algorithm to identify conditions under which, a quantum advantage
is realised. A data dependent projected quantum kernel was shown to provide
significant advantage over classical kernels. Further, we present results of
investigations and ideas pertaining to extending the use of quantum kernels as
a feature extraction layer in a Convolutional Neural Networks (CNN) that is a
widely used architecture in deep-learning applications.
