# QDC: Quantum Diffusion Convolution Kernels on Graphs

arXiv: https://arxiv.org/abs/2307.11234 · HTML: https://mlsanity.com/paper/2307.11234/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 64 references that are in the map.
- First posted on arXiv 20 Jul 2023.

## Builds on (most cited first, 29 of 29)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [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)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Alleviating the Inconsistency Problem of Applying Graph Neural Network to Fraud Detection](https://mlsanity.com/paper/2005.00625/) (2020)
- [Molecular graph generation with Graph Neural Networks](https://mlsanity.com/paper/2012.07397/) (2020)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Multi-level Graph Convolutional Networks for Cross-platform Anchor Link Prediction](https://mlsanity.com/paper/2006.01963/) (2020)
- [Unveiling the potential of Graph Neural Networks for network modeling and optimization in SDN](https://mlsanity.com/paper/1901.08113/) (2019)
- [Reliable Graph Neural Networks for Drug Discovery Under Distributional Shift](https://mlsanity.com/paper/2111.12951/) (2021)
- [TransGCN:Coupling Transformation Assumptions with Graph Convolutional Networks for Link Prediction](https://mlsanity.com/paper/1910.00702/) (2019)
- [HiSTGNN: Hierarchical Spatio-temporal Graph Neural Networks for Weather Forecasting](https://mlsanity.com/paper/2201.09101/) (2022)
- [Graph Neural Networks in Computer Vision -- Architectures, Datasets and Common Approaches](https://mlsanity.com/paper/2212.10207/) (2022)

## Built on by (most cited first, 4 of 4)

- [On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems](https://mlsanity.com/paper/2405.01009/) (2024)
- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challenges](https://mlsanity.com/paper/2311.07073/) (2023)
- [Improving the Effective Receptive Field of Message-Passing Neural Networks](https://mlsanity.com/paper/2505.23185/) (2025)

## 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.