# Defining Quantum Neural Networks via Quantum Time Evolution

arXiv: https://arxiv.org/abs/1905.10912 · HTML: https://mlsanity.com/paper/1905.10912/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2019.

## Built on by (most cited first, 8 of 8)

- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [QClusformer: A Quantum Transformer-based Framework for Unsupervised Visual Clustering](https://mlsanity.com/paper/2405.19722/) (2024)
- [QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networks](https://mlsanity.com/paper/2507.05190/) (2025)
- [varphi-Adapt: A Physics-Informed Adaptation Learning Approach to 2D Quantum Material Discovery](https://mlsanity.com/paper/2507.05184/) (2025)
- [QuPAINT: Physics-Aware Instruction Tuning Approach to Quantum Material Discovery](https://mlsanity.com/paper/2602.17478/) (2026)
- [CLIFF: Continual Learning for Incremental Flake Features in 2D Material Identification](https://mlsanity.com/paper/2508.17261/) (2025)
- [OpenQlaw: An Agentic AI Assistant for Analysis of 2D Quantum Materials](https://mlsanity.com/paper/2603.17043/) (2026)
- [QuPAINT: Physics-Aware Multimodal Reasoning for Quantum Material Characterization](https://mlsanity.com/paper/2609.12202/) (2026)

## Abstract (arXiv)

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.