# Quantum Graph Learning: Frontiers and Outlook

arXiv: https://arxiv.org/abs/2302.00892 · HTML: https://mlsanity.com/paper/2302.00892/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 71 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 18 of 18)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [A divide-and-conquer algorithm for quantum state preparation](https://mlsanity.com/paper/2008.01511/) (2020)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Graph Convolutional Neural Networks based on Quantum Vertex Saliency](https://mlsanity.com/paper/1809.01090/) (2018)
- [Multivariate Relations Aggregation Learning in Social Networks](https://mlsanity.com/paper/2008.03654/) (2020)
- [Graph Augmentation Learning](https://mlsanity.com/paper/2203.09020/) (2022)
- [Towards Quantum Graph Neural Networks: An Ego-Graph Learning Approach](https://mlsanity.com/paper/2201.05158/) (2022)
- [Big Networks: A Survey](https://mlsanity.com/paper/2008.03638/) (2020)
- [From Quantum Graph Computing to Quantum Graph Learning: A Survey](https://mlsanity.com/paper/2202.09506/) (2022)
- [Detecting Outlier Patterns with Query-based Artificially Generated Searching Conditions](https://mlsanity.com/paper/2204.02676/) (2022)
- [CHIEF: Clustering with Higher-order Motifs in Big Networks](https://mlsanity.com/paper/2204.02656/) (2022)

## Built on by (most cited first, 6 of 6)

- [Biologically Plausible Brain Graph Transformer](https://mlsanity.com/paper/2502.08958/) (2025)
- [GQWformer: A Quantum-based Transformer for Graph Representation Learning](https://mlsanity.com/paper/2412.02285/) (2024)
- [Learnable quantum spectral filters for hybrid graph neural networks](https://mlsanity.com/paper/2507.05640/) (2025)
- [A Laplacian-based Quantum Graph Neural Network for Semi-Supervised Learning](https://mlsanity.com/paper/2408.05498/) (2024)
- [Can Geometric Quantum Machine Learning Lead to Advantage in Barcode Classification?](https://mlsanity.com/paper/2409.01496/) (2024)
- [Enhancement of Quantum Semi-Supervised Learning via Improved Laplacian and Poisson Methods](https://mlsanity.com/paper/2508.02054/) (2025)

## Abstract (arXiv)

Quantum theory has shown its superiority in enhancing machine learning. However, facilitating quantum theory to enhance graph learning is in its infancy. This survey investigates the current advances in quantum graph learning (QGL) from three perspectives, i.e., underlying theories, methods, and prospects. We first look at QGL and discuss the mutualism of quantum theory and graph learning, the specificity of graph-structured data, and the bottleneck of graph learning, respectively. A new taxonomy of QGL is presented, i.e., quantum computing on graphs, quantum graph representation, and quantum circuits for graph neural networks. Pitfall traps are then highlighted and explained. This survey aims to provide a brief but insightful introduction to this emerging field, along with a detailed discussion of frontiers and outlook yet to be investigated.