# From Quantum Graph Computing to Quantum Graph Learning: A Survey

arXiv: https://arxiv.org/abs/2202.09506 · HTML: https://mlsanity.com/paper/2202.09506/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 82 references that are in the map.
- First posted on arXiv 19 Feb 2022.

## Builds on (most cited first, 21 of 21)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [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)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [Convolutional Kernel Networks for Graph-Structured Data](https://mlsanity.com/paper/2003.05189/) (2020)
- [Hybrid Quantum-Classical Graph Convolutional Network](https://mlsanity.com/paper/2101.06189/) (2021)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Quantum Graph Convolutional Neural Networks](https://mlsanity.com/paper/2107.03257/) (2021)
- [Graph Convolutional Neural Networks based on Quantum Vertex Saliency](https://mlsanity.com/paper/1809.01090/) (2018)
- [Rethinking Kernel Methods for Node Representation Learning on Graphs](https://mlsanity.com/paper/1910.02548/) (2019)
- [A Review of Machine Learning Classification Using Quantum Annealing for Real-world Applications](https://mlsanity.com/paper/2106.02964/) (2021)
- [A quantum algorithm for training wide and deep classical neural networks](https://mlsanity.com/paper/2107.09200/) (2021)
- [Quantum Speedups for Exponential-Time Dynamic Programming Algorithms](https://mlsanity.com/paper/1807.05209/) (2018)

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

- [Quantum Graph Learning: Frontiers and Outlook](https://mlsanity.com/paper/2302.00892/) (2023)
- [GQWformer: A Quantum-based Transformer for Graph Representation Learning](https://mlsanity.com/paper/2412.02285/) (2024)
- [Extending Graph Transformers with Quantum Computed Aggregation](https://mlsanity.com/paper/2210.10610/) (2022)
- [Enhancement of Quantum Semi-Supervised Learning via Improved Laplacian and Poisson Methods](https://mlsanity.com/paper/2508.02054/) (2025)

## Abstract (arXiv)

Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational power. In this paper, we provide a targeted survey of the development of QC for graph-related tasks. We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions that can not be produced by classical systems efficiently for some problems related to graphs. For its practicability and wide-applicability, we give a brief review of typical graph learning techniques designed for various tasks. Inspired by these powerful methods, we note that advanced quantum algorithms have been proposed for characterizing the graph structures. We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research. We further discuss the challenges of using quantum algorithms in graph learning, and future directions towards more flexible and versatile quantum graph learning solvers.