  This work presents a novel fundamental algorithm for for defining and
training Neural Networks in Quantum Information based on time evolution and the
Hamiltonian. Classical Neural Network algorithms (ANN) are computationally
expensive. For example, in image classification, representing an image pixel by
pixel using classical information requires an enormous amount of computational
memory resources. Hence, exploring methods to represent images in a different
paradigm of information is important. Quantum Neural Networks (QNNs) have been
explored for over 20 years. The current forefront work based on Variational
Quantum Circuits is specifically defined for the Continuous Variable (CV) Model
of quantum computers. In this work, a model is proposed which is defined at a
more fundamental level and hence can be inherited by any variants of quantum
computing models. This work also presents a quantum backpropagation algorithm
to train our QNN model and validate this algorithm on the MNIST dataset on a
quantum computer simulation.
