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

A method for analyzing and synthesizing the feature map for the kernel-based quantum classifier is developed, using the Pauli decomposition. In particular, for 2-dimensional input datasets, the method boils down to a general formula that easily computes a lower bound of the exact training accuracy, which eventually helps us to see whether the selected feature map is suitable for linearly separating the dataset. Also, a synthesis method, that combines different kernels to construct a better-performing feature map in a lager feature space, is demonstrated.