mlsanityData to 7 Oct 2026

QDC: Quantum Diffusion Convolution Kernels on Graphs

arXiv 2307.11234 ↗First posted 20 Jul 2023cs.LG quant-phcited by 4

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Abstract (arXiv)

Graph convolutional neural networks (GCNs) operate by aggregating messages over local neighborhoods given the prediction task under interest. Many GCNs can be understood as a form of generalized diffusion of input features on the graph, and significant work has been dedicated to improving predictive accuracy by altering the ways of message passing. In this work, we propose a new convolution kernel that effectively rewires the graph according to the occupation correlations of the vertices by trading on the generalized diffusion paradigm for the propagation of a quantum particle over the graph. We term this new convolution kernel the Quantum Diffusion Convolution (QDC) operator. In addition, we introduce a multiscale variant that combines messages from the QDC operator and the traditional combinatorial Laplacian. To understand our method, we explore the spectral dependence of homophily and the importance of quantum dynamics in the construction of a bandpass filter. Through these studies, as well as experiments on a range of datasets, we observe that QDC improves predictive performance on the widely used benchmark datasets when compared to similar methods.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 29 of its 64 references that are in the map. First posted on arXiv 20 Jul 2023.

Builds on

29 of 64 references.

References · 29

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  5. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  6. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  7. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,133
  8. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  9. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  10. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 624
  11. 2020Graph Neural Networks in Recommender Systems: A Surveycited by 493
  12. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
17 more
  1. 2019Diffusion Improves Graph Learningcited by 414
  2. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  3. 2021GRAND: Graph Neural Diffusioncited by 258
  4. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  5. 2022Forecasting Global Weather with Graph Neural Networkscited by 165
  6. 2021A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directionscited by 144
  7. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  8. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  9. 2020Alleviating the Inconsistency Problem of Applying Graph Neural Network to Fraud Detectioncited by 81
  10. 2020Molecular graph generation with Graph Neural Networkscited by 79
  11. 2020Graph Convolutional Networks using Heat Kernel for Semi-supervised Learningcited by 50
  12. 2020Multi-level Graph Convolutional Networks for Cross-platform Anchor Link Predictioncited by 30
  13. 2019Unveiling the potential of Graph Neural Networks for network modeling and optimization in SDNcited by 27
  14. 2021Reliable Graph Neural Networks for Drug Discovery Under Distributional Shiftcited by 22
  15. 2019TransGCN:Coupling Transformation Assumptions with Graph Convolutional Networks for Link Predictioncited by 17
  16. 2022HiSTGNN: Hierarchical Spatio-temporal Graph Neural Networks for Weather Forecastingcited by 5
  17. 2022Graph Neural Networks in Computer Vision -- Architectures, Datasets and Common Approachescited by 4

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Cited by year

Citing papers per year: 2023: 2; 2024: 1; 2025: 1.

4 papers.

  1. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  2. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 26
  3. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  4. 2025Improving the Effective Receptive Field of Message-Passing Neural Networkscited by 6