Quantum Principal Basis Learning for image classification

This work presents a preliminary framework to learn the basis transformationthat makes the principal components of the same label featuresof the principal components that are present in a superposition of imagesthat share patterns, or in other words, they have the same label. In other wordsis designed to learn the basis transformation for which the images of the sameclass have the same principal components. The optimization is then based on thechoice of the basis transformation that better describes the principal componentsof all the images that share the same label. The learning of the basis differs fromthe traditional QNN in the sense that the learning is in what operators mustbe present in the basis representation using controlled-U, and the parametersare then a bit string of what gates must be activated or not for each basistransformation.