# A unifying primary framework for quantum graph neural networks from quantum graph states

arXiv: https://arxiv.org/abs/2402.13001 · HTML: https://mlsanity.com/paper/2402.13001/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 22 of 22)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [Evaluating Graph Neural Networks for Link Prediction: Current Pitfalls and New Benchmarking](https://mlsanity.com/paper/2306.10453/) (2023)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [Financial Fraud Detection using Quantum Graph Neural Networks](https://mlsanity.com/paper/2309.01127/) (2023)
- [Hybrid Quantum-Classical Graph Convolutional Network](https://mlsanity.com/paper/2101.06189/) (2021)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Quantum Graph Convolutional Neural Networks](https://mlsanity.com/paper/2107.03257/) (2021)
- [Towards Quantum Graph Neural Networks: An Ego-Graph Learning Approach](https://mlsanity.com/paper/2201.05158/) (2022)
- [A Simple Quantum Neural Net with a Periodic Activation Function](https://mlsanity.com/paper/1804.07633/) (2018)
- [Quantum implementation of circulant matrices and its use in quantum string processing](https://mlsanity.com/paper/2206.09364/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learnable quantum spectral filters for hybrid graph neural networks](https://mlsanity.com/paper/2507.05640/) (2025)

## Abstract (arXiv)

Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural network model can be understood and realized based on graph states. We show that they can be used either as a parameterized quantum circuits to represent neural networks or as an underlying structure to construct graph neural networks on quantum computers.