Classification of NEQR Processed Classical Images using Quantum Neural Networks (QNN)

A quantum neural network (QNN) is interpreted today as any quantum circuit with trainable continuous parameters. This work builds on previous works by the authors and addresses QNN for image classification with Novel Enhanced Quantum Representation of (NEQR) processed classical data where Principal component analysis (PCA) and Projected Quantum Kernel features (PQK) were investigated previously by the authors as a path to quantum advantage for the same classical dataset. For each of these cases the Fashion-MNIST dataset was downscaled using PCA to convert into quantum data where the classical NN easily outperformed the QNN. However, we demonstrated quantum advantage by using PQK where quantum models achieved more than ~90% accuracy surpassing their classical counterpart on the same training dataset as in the first case. In this current work, we use the same dataset fed into a QNN and compare that with performance of a classical NN model. We built an NEQR model circuit to pre-process the same data and feed the images into the QNN. Our results showed marginal improvements (only about ~5.0%) where the QNN performance with NEQR exceeded the performance of QNN without NEQR. We conclude that given the computational cost and the massive circuit depth associated with running NEQR, the advantage offered by this specific Quantum Image Processing (QIMP) algorithm is questionable at least for classical image dataset. No actual quantum computing hardware platform exists today that can support the circuit depth needed to run NEQR even for the reduced image sizes of our toy classical dataset.