# Quantum Graph Neural Networks

arXiv: https://arxiv.org/abs/1909.12264 · HTML: https://mlsanity.com/paper/1909.12264/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2019.

## Built on by (most cited first, 30 of 66)

- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Graph neural network initialisation of quantum approximate optimisation](https://mlsanity.com/paper/2111.03016/) (2021)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data](https://mlsanity.com/paper/2306.07331/) (2023)
- [Reinforcement learning-assisted quantum architecture search for variational quantum algorithms](https://mlsanity.com/paper/2402.13754/) (2024)
- [A Leap among Quantum Computing and Quantum Neural Networks: A Survey](https://mlsanity.com/paper/2107.03313/) (2021)
- [Towards Quantum Graph Neural Networks: An Ego-Graph Learning Approach](https://mlsanity.com/paper/2201.05158/) (2022)
- [Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks](https://mlsanity.com/paper/2406.18316/) (2024)
- [On the universality of Sn-equivariant k-body gates](https://mlsanity.com/paper/2303.00728/) (2023)
- [AutoQML: Automated Quantum Machine Learning for Wi-Fi Integrated Sensing and Communications](https://mlsanity.com/paper/2205.09115/) (2022)
- [Quantum Graph Learning: Frontiers and Outlook](https://mlsanity.com/paper/2302.00892/) (2023)
- [A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networks](https://mlsanity.com/paper/2311.18672/) (2023)
- [From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks](https://mlsanity.com/paper/2408.06524/) (2024)
- [Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gating](https://mlsanity.com/paper/2301.08173/) (2023)
- [From Quantum Graph Computing to Quantum Graph Learning: A Survey](https://mlsanity.com/paper/2202.09506/) (2022)
- [Quantum Transfer Learning for Wi-Fi Sensing](https://mlsanity.com/paper/2205.08590/) (2022)
- [Graph Neural Networks on Quantum Computers](https://mlsanity.com/paper/2405.17060/) (2024)
- [Resource-efficient equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2410.01252/) (2024)
- [Training Hybrid Classical-Quantum Classifiers via Stochastic Variational Optimization](https://mlsanity.com/paper/2201.08629/) (2022)
- [An Empirical Review of Optimization Techniques for Quantum Variational Circuits](https://mlsanity.com/paper/2202.01389/) (2022)
- [Classical ensemble of Quantum-classical ML algorithms for Phishing detection in Ethereum transaction networks](https://mlsanity.com/paper/2211.00004/) (2022)

## Abstract (arXiv)

We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable to be executed on distributed quantum systems over a quantum network. Along with this general class of ansatze, we introduce further specialized architectures, namely, Quantum Graph Recurrent Neural Networks (QGRNN) and Quantum Graph Convolutional Neural Networks (QGCNN). We provide four example applications of QGNNs: learning Hamiltonian dynamics of quantum systems, learning how to create multipartite entanglement in a quantum network, unsupervised learning for spectral clustering, and supervised learning for graph isomorphism classification.