# Inductive Graph Representation Learning with Quantum Graph Neural Networks

arXiv: https://arxiv.org/abs/2503.24111 · HTML: https://mlsanity.com/paper/2503.24111/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 67 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Builds on (most cited first, 30 of 40)

- [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)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks](https://mlsanity.com/paper/2012.07690/) (2020)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [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)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [LiGNN: Graph Neural Networks at LinkedIn](https://mlsanity.com/paper/2402.11139/) (2024)
- [QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules](https://mlsanity.com/paper/2306.09549/) (2023)

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

- [Quantum Graph Attention Networks: Trainable Quantum Encoders for Inductive Graph Learning](https://mlsanity.com/paper/2509.11390/) (2025)

## Abstract (arXiv)

Graph Neural Networks (QGNNs) offer a promising approach to combining quantum computing with graph-structured data processing. While classical Graph Neural Networks (GNNs) are scalable and robust, existing QGNNs often lack flexibility due to graph-specific quantum circuit designs, limiting their applicability to diverse real-world problems. To address this, we propose a versatile QGNN framework inspired by GraphSAGE, using quantum models as aggregators to generate quantum-native node embeddings. We integrate inductive representation learning techniques with parameterized quantum convolutional and pooling layers, bridging classical and quantum paradigms. The convolutional layer is flexible, allowing tailored designs for specific tasks. Benchmarked on a node regression task with the QM9 dataset, our framework, using a single minimal circuit for all aggregation steps, handles molecules with varying numbers of atoms without changing qubits or circuit architecture. While classical GNNs achieve higher training performance, our quantum approach remains competitive and often shows enhanced generalization as molecular complexity increases. We also observe faster learning in early training epochs. To mitigate trainability limitations of a single-circuit setup, we extend the framework with multiple quantum aggregators on QM9. Assigning distinct circuits to each hop substantially improves training performance across all cases. Additionally, we numerically demonstrate the absence of barren plateaus as qubit numbers increase, suggesting that the proposed model remains trainable to larger, more complex graph-based problems.