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This work presents a novel fundamental algorithm for for defining andtraining Neural Networks in Quantum Information based on time evolution and theHamiltonian. Classical Neural Network algorithms (ANN) are computationallyexpensive. For example, in image classification, representing an image pixel bypixel using classical information requires an enormous amount of computationalmemory resources. Hence, exploring methods to represent images in a differentparadigm of information is important. Quantum Neural Networks (QNNs) have beenexplored for over 20 years. The current forefront work based on VariationalQuantum Circuits is specifically defined for the Continuous Variable (CV) Modelof quantum computers. In this work, a model is proposed which is defined at amore fundamental level and hence can be inherited by any variants of quantumcomputing models. This work also presents a quantum backpropagation algorithmto train our QNN model and validate this algorithm on the MNIST dataset on aquantum computer simulation.

Defining Quantum Neural Networks via Quantum Time Evolution