Analysis and synthesis of feature map for kernel-based quantum classifier

A method for analyzing the feature map for the kernel-based quantum classifier is developed; that is, we give a general formula for computing a lower bound of the exact training accuracy, which helps us to see whether the selected feature map is suitable for linearly separating the dataset. We show a proof of concept demonstration of this method for a class of 2-qubit classifier, with several 2-dimensional dataset. Also, a synthesis method, that combines different kernels to construct a better-performing feature map in a lager feature space, is presented.