# Hybrid Quantum-Classical Graph Convolutional Network

arXiv: https://arxiv.org/abs/2101.06189 · HTML: https://mlsanity.com/paper/2101.06189/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 90 references that are in the map.
- First posted on arXiv 15 Jan 2021.

## Builds on (most cited first, 30 of 35)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [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)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [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)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecasting](https://mlsanity.com/paper/1802.07007/) (2018)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Quantum Convolutional Neural Networks for High Energy Physics Data Analysis](https://mlsanity.com/paper/2012.12177/) (2020)
- [Decentralizing Feature Extraction with Quantum Convolutional Neural Network for Automatic Speech Recognition](https://mlsanity.com/paper/2010.13309/) (2020)
- [Jet-Images -- Deep Learning Edition](https://mlsanity.com/paper/1511.05190/) (2015)
- [Parameterized Machine Learning for High-Energy Physics](https://mlsanity.com/paper/1601.07913/) (2016)
- [Quantum-inspired Machine Learning on high-energy physics data](https://mlsanity.com/paper/2004.13747/) (2020)
- [Semi-supervised User Geolocation via Graph Convolutional Networks](https://mlsanity.com/paper/1804.08049/) (2018)
- [A Convolutional Neural Network Neutrino Event Classifier](https://mlsanity.com/paper/1604.01444/) (2016)

## Built on by (most cited first, 21 of 21)

- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [Quantum machine learning with differential privacy](https://mlsanity.com/paper/2103.06232/) (2021)
- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [Quantum Architecture Search via Continual Reinforcement Learning](https://mlsanity.com/paper/2112.05779/) (2021)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)
- [Unravelling physics beyond the standard model with classical and quantum anomaly detection](https://mlsanity.com/paper/2301.10787/) (2023)
- [Towards Quantum Graph Neural Networks: An Ego-Graph Learning Approach](https://mlsanity.com/paper/2201.05158/) (2022)
- [3D-QAE: Fully Quantum Auto-Encoding of 3D Point Clouds](https://mlsanity.com/paper/2311.05604/) (2023)
- [From Quantum Graph Computing to Quantum Graph Learning: A Survey](https://mlsanity.com/paper/2202.09506/) (2022)
- [mathbbZ2× mathbbZ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks](https://mlsanity.com/paper/2311.18744/) (2023)
- [Equivariant Quantum Graph Circuits](https://mlsanity.com/paper/2112.05261/) (2021)
- [Optimizing Quantum Convolutional Neural Network Architectures for Arbitrary Data Dimension](https://mlsanity.com/paper/2403.19099/) (2024)
- [A unifying primary framework for quantum graph neural networks from quantum graph states](https://mlsanity.com/paper/2402.13001/) (2024)
- [Learnable quantum spectral filters for hybrid graph neural networks](https://mlsanity.com/paper/2507.05640/) (2025)
- [Quantum Privacy Aggregation of Teacher Ensembles (QPATE) for Privacy-preserving Quantum Machine Learning](https://mlsanity.com/paper/2401.07464/) (2024)
- [A Spatio-Temporal Hybrid Quantum-Classical Graph Convolutional Neural Network Approach for Urban Taxi Destination Prediction](https://mlsanity.com/paper/2512.13745/) (2025)
- [Edge-Local and Qubit-Efficient Quantum Graph Learning for the NISQ Era](https://mlsanity.com/paper/2602.16018/) (2026)

## Abstract (arXiv)

The high energy physics (HEP) community has a long history of dealing with large-scale datasets. To manage such voluminous data, classical machine learning and deep learning techniques have been employed to accelerate physics discovery. Recent advances in quantum machine learning (QML) have indicated the potential of applying these techniques in HEP. However, there are only limited results in QML applications currently available. In particular, the challenge of processing sparse data, common in HEP datasets, has not been extensively studied in QML models. This research provides a hybrid quantum-classical graph convolutional network (QGCNN) for learning HEP data. The proposed framework demonstrates an advantage over classical multilayer perceptron and convolutional neural networks in the aspect of number of parameters. Moreover, in terms of testing accuracy, the QGCNN shows comparable performance to a quantum convolutional neural network on the same HEP dataset while requiring less than 50% of the parameters. Based on numerical simulation results, studying the application of graph convolutional operations and other QML models may prove promising in advancing HEP research and other scientific fields.