# From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks

arXiv: https://arxiv.org/abs/2408.06524 · HTML: https://mlsanity.com/paper/2408.06524/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 178 references that are in the map.
- First posted on arXiv 12 Aug 2024.

## Builds on (most cited first, 30 of 63)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)

## Built on by (most cited first, 6 of 6)

- [Learnable quantum spectral filters for hybrid graph neural networks](https://mlsanity.com/paper/2507.05640/) (2025)
- [Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchy](https://mlsanity.com/paper/2606.26873/) (2026)
- [Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning](https://mlsanity.com/paper/2607.00063/) (2026)
- [QGraphLIME - Explaining Quantum Graph Neural Networks](https://mlsanity.com/paper/2510.05683/) (2025)
- [Optimizing Quantum Key Distribution Network Performance using Graph Neural Networks](https://mlsanity.com/paper/2511.16468/) (2025)
- [Analog Quantum Asynchronous Event-Based Graph Neural Network](https://mlsanity.com/paper/2606.11000/) (2026)

## Abstract (arXiv)

Quantum Graph Neural Networks (QGNNs) represent a novel fusion of quantum computing and Graph Neural Networks (GNNs), aimed at overcoming the computational and scalability challenges inherent in classical GNNs that are powerful tools for analyzing data with complex relational structures but suffer from limitations such as high computational complexity and over-smoothing in large-scale applications. Quantum computing, leveraging principles like superposition and entanglement, offers a pathway to enhanced computational capabilities. This paper critically reviews the state-of-the-art in QGNNs, exploring various architectures. We discuss their applications across diverse fields such as high-energy physics, molecular chemistry, finance and earth sciences, highlighting the potential for quantum advantage. Additionally, we address the significant challenges faced by QGNNs, including noise, decoherence, and scalability issues, proposing potential strategies to mitigate these problems. This comprehensive review aims to provide a foundational understanding of QGNNs, fostering further research and development in this promising interdisciplinary field.