# Graph Convolutional Neural Networks based on Quantum Vertex Saliency

arXiv: https://arxiv.org/abs/1809.01090 · HTML: https://mlsanity.com/paper/1809.01090/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2018.

## Built on by (most cited first, 12 of 12)

- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [Heterophily-Aware Graph Attention Network](https://mlsanity.com/paper/2302.03228/) (2023)
- [A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizability](https://mlsanity.com/paper/2406.09031/) (2024)
- [Quantum Graph Learning: Frontiers and Outlook](https://mlsanity.com/paper/2302.00892/) (2023)
- [From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks](https://mlsanity.com/paper/2408.06524/) (2024)
- [From Quantum Graph Computing to Quantum Graph Learning: A Survey](https://mlsanity.com/paper/2202.09506/) (2022)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)
- [LGAN: An Efficient High-Order Graph Neural Network via the Line Graph Aggregation](https://mlsanity.com/paper/2512.10735/) (2025)
- [AKBR: Learning Adaptive Kernel-based Representations for Graph Classification](https://mlsanity.com/paper/2403.16130/) (2024)
- [HC-GAE: The Hierarchical Cluster-based Graph Auto-Encoder for Graph Representation Learning](https://mlsanity.com/paper/2405.14742/) (2024)
- [A Spatio-Temporal Hybrid Quantum-Classical Graph Convolutional Neural Network Approach for Urban Taxi Destination Prediction](https://mlsanity.com/paper/2512.13745/) (2025)
- [Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables](https://mlsanity.com/paper/2605.13383/) (2026)

## Abstract (arXiv)

This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transitive aligned vertices between graphs, and transforms arbitrary sized graphs into fixed-sized aligned vertex grid structures. In order to learn representative graph characteristics, a new quantum spatial graph convolution is proposed and employed to extract multi-scale vertex features, in terms of quantum information propagation between grid vertices of each graph. Since the quantum spatial convolution preserves the grid structures of the input vertices (i.e., the convolution layer does not change the original spatial sequence of vertices), the proposed QSGCNN model allows to directly employ the traditional convolutional neural network architecture to further learn from the global graph topology, providing an end-to-end deep learning architecture that integrates the graph representation and learning in the quantum spatial graph convolution layer and the traditional convolutional layer for graph classifications. We demonstrate the effectiveness of the proposed QSGCNN model in relation to existing state-of-the-art methods. The proposed QSGCNN model addresses the shortcomings of information loss and imprecise information representation arising in existing GCN models associated with the use of SortPooling or SumPooling layers. Experiments on benchmark graph classification datasets demonstrate the effectiveness of the proposed QSGCNN model.