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# 🔄 Quantum Graph Learning (QGraph) Papers

This section of the **Quantum AI Papers** repository focuses on **Quantum Graph Learning (QGraph)**.  
QTL leverages knowledge from pre-trained quantum or hybrid quantum-classical models and adapts it to new tasks or domains. This paradigm plays a crucial role in overcoming limitations of small datasets, reducing training costs, and accelerating the deployment of quantum-enhanced AI systems.

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## 📚 Scope
Research papers in this category explore:
- Transfer of learned quantum circuit parameters between tasks  
- Hybrid classical–quantum transfer learning frameworks  
- Applications of QTL in physics, chemistry, medical imaging, and natural language processing  
- Optimization strategies to mitigate issues such as barren plateaus  
- Cross-domain transfer of quantum models for practical real-world problems

---

## 🗂️ Papers List

| title                                                                                                                       |   year | publisher                                                                                     | Author                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      | link                                                                                                                        | category   |
|:----------------------------------------------------------------------------------------------------------------------------|-------:|:----------------------------------------------------------------------------------------------|:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:----------------------------------------------------------------------------------------------------------------------------|:-----------|
| Quantum graphs: Different perspectives, homomorphisms and quantum automorphisms                                             |   2024 | Communications of the American Mathematical Society                                           | Daws, Matthew.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | https://www.ams.org/journals/cams/2024-04-05/S2692-3688-2024-00030-5/                                                       | Qgraph     |
| Algebraic Connectedness and Bipartiteness of Quantum Graphs                                                                 |   2024 | Communications in Mathematical Physics                                                        | Matsuda, Junichiro.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         | https://link.springer.com/article/10.1007/s00220-024-05046-y                                                                | Qgraph     |
| Financial fraud detection using quantum graph neural networks                                                               |   2024 | Quantum Machine Intelligence                                                                  | Innan, Nouhaila, et al.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | https://link.springer.com/article/10.1007/s42484-024-00143-6                                                                | Qgraph     |
| A Comparison between Invariant and Equivariant Classical and Quantum Graph Neural Networks                                  |   2024 | Axioms                                                                                        | Forestano, Roy T., et al.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   | https://www.mdpi.com/2075-1680/13/3/160                                                                                     | Qgraph     |
| Deep quantum graph dreaming: deciphering neural network insights into quantum experiments                                   |   2024 | Machine Learning: Science and Technology                                                      | Jaouni, Tareq, et al.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | https://iopscience.iop.org/article/10.1088/2632-2153/ad2628/meta                                                            | Qgraph     |
| Time evolution and the Schrödinger equation on                                                                              |   2024 | Journal of Physics A: Mathematical and Theoretical                                            | Smilansky, Uzy, and Gilad Sofer.                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | https://iopscience.iop.org/article/10.1088/1751-8121/ad1fb6/meta                                                            | Qgraph     |
| time dependent quantum graphs                                                                                               |        |                                                                                               |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                             |            |
| Invariants of the quantum graph of the partial trace                                                                        |   2024 | arXiv                                                                                         | Paupa, Wojciech, and Piotr M. Sołtan.                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | https://arxiv.org/abs/2408.16858                                                                                            | Qgraph     |
| QBER: Quantum-based Entropic Representations for un-attributed graphs                                                       |   2024 | Pattern Recognition 1                                                                         | Cui, Lixin, et al.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | https://www.sciencedirect.com/science/article/abs/pii/S0031320323005757                                                     | Qgraph     |
| Quantum isomorphism of graphs from association schemes                                                                      |   2024 | Journal of Combinatorial Theory                                                               | Chan, Ada, and William J. Martin.                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | https://www.sciencedirect.com/science/article/abs/pii/S0095895623000813                                                     | Qgraph     |
| HAQJSK: Hierarchical-Aligned Quantum Jensen-Shannon Kernels for Graph Classification                                        |   2024 | IEEE Transactions on Knowledge and Data Engineering                                           | Bai, Lu, et al.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | https://ieeexplore.ieee.org/abstract/document/10502132                                                                      | Qgraph     |
| A Quantum Spatial Graph Convolutional Neural Network Model on Quantum Circuits                                              |   2024 | IEEE Transactions on Neural Networks and Learning Systems                                     | Zheng, Jin, et al.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | https://ieeexplore.ieee.org/abstract/document/10499715                                                                      | Qgraph     |
| Quantum Feature Embeddings for Graph Neural Networks                                                                        |   2024 | HICSS                                                                                         | Xu, Sascha, Frank Wilhelm-Mauch, and Wolfgang Maass.                                                                                                                                                                                                                                                                                                                                                                                                                                                        | https://www.quasim-project.de/wp-content/uploads/2023/09/Quantum-Feature-Embeddings-for-Graph-Neural-Networks_HICSS2024.pdf | Qgraph     |
| Quantum Positional Encodings for Graph Neural Networks                                                                      |   2024 | arXiv                                                                                         | Thabet, Slimane, et al.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | https://arxiv.org/abs/2406.06547                                                                                            | Qgraph     |
| GraphiQ: Quantum circuit design for photonic graph states                                                                   |   2024 | arXiv                                                                                         | Lin, Jie, et al.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | https://arxiv.org/abs/2402.09285                                                                                            | Qgraph     |
| Interaction graph-based characterization of quantum benchmarks for improving quantum circuit mapping techniques             |   2023 | Springer                                                                                      | Medina Bandic, Carmen G. Almudever, Sebastian Feld                                                                                                                                                                                                                                                                                                                                                                                                                                                          | https://doi.org/10.1007/s42484-023-00124-1                                                                                  | Qgraph     |
| Very-large-scale integrated quantum graph photonics                                                                         |   2023 | Nature Photonics                                                                              | Jueming Bao, Zhaorong Fu, Tanumoy Pramanik, Jun Mao, Yulin Chi, Yingkang Cao, Chonghao Zhai, Yifei Mao, Tianxiang Dai, Xiaojiong Chen, Xinyu Jia, Leshi Zhao, Yun Zheng, Bo Tang, Zhihua Li, Jun Luo, Wenwu Wang, Yan Yang, Yingying Peng, Dajian Liu, Daoxin Dai, Qiongyi He, Alif Laila Muthali, Leif K. Oxenløwe, Caterina Vigliar, Stefano Paesani, Huili Hou, Raffaele Santagati, Joshua W. Silverstone, Anthony Laing, Mark G. Thompson, Jeremy L. O’Brien, Yunhong Ding, Qihuang Gong & Jianwei Wang | https://doi.org/10.1038/s41566-023-01187-z                                                                                  | Qgraph     |
| GCS-Q: Quantum Graph Coalition Structure Generation                                                                         |   2023 | Springer                                                                                      | Supreeth Mysore Venkatesh, Antonio Macaluso & Matthias Klusch                                                                                                                                                                                                                                                                                                                                                                                                                                               | https://doi.org/10.1007/978-3-031-36030-5_11                                                                                | Qgraph     |
| Deep learning metal complex properties with natural quantum graphs                                                          |   2023 | ROYAL SOCIETY OF CHEMISTRY                                                                    | Hannes Kneiding, Ruslan Lukin a, Lucas Lang , Simen Reine logoa, Thomas Bondo Pedersen, Riccardo De Bin , David Balcells                                                                                                                                                                                                                                                                                                                                                                                    | https://doi.org/10.1039/D2DD00129B                                                                                          | Qgraph     |
| Distinguishing cospectral quantum graphs by scattering                                                                      |   2023 | IOPSCIENCE                                                                                    | Delio Mugnolo and Vyacheslav Pivovarchik                                                                                                                                                                                                                                                                                                                                                                                                                                                                    | https://doi.org/10.1088/1751-8121/acbb44                                                                                    | Qgraph     |
| Equivariant quantum circuits for learning on weighted graphs                                                                |   2023 | npj Quantum Information                                                                       | Andrea Skolik, Michele Cattelan, Sheir Yarkoni, Thomas Bäck & Vedran Dunjko                                                                                                                                                                                                                                                                                                                                                                                                                                 | https://doi.org/10.1038/s41534-023-00710-y                                                                                  | Qgraph     |
| Quantum feature maps for graph machine learning on a neutral atom quantum processor                                         |   2023 | APS                                                                                           | Boris Albrecht, Constantin Dalyac, Lucas Leclerc, Luis Ortiz-Gutiérrez, Slimane Thabet, Mauro D'Arcangelo, Julia R. K. Cline, Vincent E. Elfving, Lucas Lassablière, Henrique Silvério, Bruno Ximenez, Louis-Paul Henry, Adrien Signoles, and Loïc Henriet                                                                                                                                                                                                                                                  | https://doi.org/10.1103/PhysRevA.107.042615                                                                                 | Qgraph     |
| Advantages and Limitations of Quantum Routing                                                                               |   2023 | APS                                                                                           | Aniruddha Bapat, Andrew M. Childs, Alexey V. Gorshkov, and Eddie Schoute                                                                                                                                                                                                                                                                                                                                                                                                                                    | https://doi.org/10.1103/PRXQuantum.4.010313                                                                                 | Qgraph     |
| Method for solving inverse spectral problems on quantum star graphs                                                         |   2023 | DE GRUYTER                                                                                    | Sergei A. Avdonin and Vladislav V. Kravchenko                                                                                                                                                                                                                                                                                                                                                                                                                                                               | https://doi.org/10.1515/jiip-2022-0045                                                                                      | Qgraph     |
| Graph-theoretical optimization of fusion-based graph state generation                                                       |   2023 | the open journal for quantum science                                                          | Seok-Hyung Lee, Hyunseok Jeong                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | https://doi.org/10.22331/q-2023-12-20-1212                                                                                  | Qgraph     |
| Quantum Automorphism Groups of Connected Locally Finite Graphs and Quantizations of Discrete Groups                         |   2023 | Journal of the American Mathematical Society                                                  | Lukas Rollier, Stefaan Vaes                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | https://doi.org/10.1093/imrn/rnad099                                                                                        | Qgraph     |
| GSQAS: Graph Self-supervised Quantum Architecture Search                                                                    |   2023 | ScienceDirect                                                                                 | Zhimin He, Maijie Deng, Shenggen Zheng, Lvzhou Li, Haozhen Situ                                                                                                                                                                                                                                                                                                                                                                                                                                             | https://doi.org/10.1016/j.physa.2023.129286                                                                                 | Qgraph     |
| On the Design of Quantum Graph Convolutional Neural Network in the NISQ-Era and Beyond                                      |   2022 | IEEE International Conference on Computer Design: VLSI in Computers and Processors, (ICCD)    | Zhirui Hu; Jinyang Li; Zhenyu Pan; Shanglin Zhou; Lei Yang; Caiwen Ding                                                                                                                                                                                                                                                                                                                                                                                                                                     | https://ieeexplore.ieee.org/abstract/document/9978396                                                                       | Qgraph     |
| Data-Driven Reliability Models of Quantum Circuit: From Traditional ML to Graph Neural Network                              |   2022 | IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems                 | Vedika Saravanan; Samah M. Saeed                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | https://ieeexplore.ieee.org/abstract/document/9877896                                                                       | Qgraph     |
| Equivariant Quantum Graph Circuits                                                                                          |   2022 | International Conference on Machine Learning                                                  | Peter Mernyei, Konstantinos Meichanetzidis, Ismail Ilkan Ceylan                                                                                                                                                                                                                                                                                                                                                                                                                                             | https://proceedings.mlr.press/v162/mernyei22a.html                                                                          | Qgraph     |
| A quantum graph approach to metamaterial design                                                                             |   2022 | Scientific Reports                                                                            | Tristan Lawrie, Gregor Tanner & Dimitrios Chronopoulos                                                                                                                                                                                                                                                                                                                                                                                                                                                      | https://www.nature.com/articles/s41598-022-22265-2                                                                          | Qgraph     |
| Temporal-Spatial Quantum Graph Convolutional Neural Network Based on Schrödinger Approach for Traffic Congestion Prediction |   2022 | IEEE Transactions on Intelligent Transportation Systems                                       | Zhiguo Qu; Xinzhu Liu; Min Zheng                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | https://ieeexplore.ieee.org/abstract/document/9882032                                                                       | Qgraph     |
| Towards Quantum Graph Neural Networks: An Ego-Graph Learning Approach                                                       |   2022 | inspirehep                                                                                    | Xing Ai(      Xiamen U.  ) , Zhihong Zhang(      Xiamen U.  ) , Luzhe Sun(      Xiamen U.  ) , Junchi Yan(      Shanghai Jiao Tong U.  ) , Edwin Hancock                                                                                                                                                                                                                                                                                                                                                    | https://inspirehep.net/literature/2011088                                                                                   | Qgraph     |
| Random quantum graphs                                                                                                       |   2022 | Trans. Amer. Math. Soc. 375 (2022)                                                            | Alexandru Chirvasitu and Mateusz Wasilewski                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | https://www.ams.org/journals/tran/2022-375-05/S0002-9947-2022-08584-6/home.html                                             | Qgraph     |
| Some examples of quantum graphs                                                                                             |   2022 | Letters in Mathematical Physics                                                               | Daniel Gromada                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | https://link.springer.com/article/10.1007/s11005-022-01603-5                                                                | Qgraph     |
| Quantum-Chemical and Quantum-Graph Models of the Dynamical Structure of CH5+                                                |   2022 | Journal of Chemical Theory and Computation                                                    | Irén Simkó, Csaba Fábri, Attila G. Császár*                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | https://pubs.acs.org/doi/abs/10.1021/acs.jctc.2c00991                                                                       | Qgraph     |
| From Quantum Graph Computing to Quantum Graph Learning: A Survey                                                            |   2022 | arxiv                                                                                         | Yehui Tang, Junchi Yan, Hancock Edwin                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | https://arxiv.org/abs/2202.09506                                                                                            | Qgraph     |
| Supervised graph classification for chiral quantum walks                                                                    |   2022 | Phys. Rev. A 105                                                                              | Artem Kryukov, Roman Abramov, Leonid E. Fedichkin, Alexander Alodjants, and Alexey A. Melnikov                                                                                                                                                                                                                                                                                                                                                                                                              | https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.022208                                                           | Qgraph     |
| Learning quantum graph states with product measurements                                                                     |   2022 | 2022 IEEE International Symposium on Information Theory (ISIT)                                | Yingkai Ouyang; Marco Tomamichel                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | https://ieeexplore.ieee.org/abstract/document/9834440                                                                       | Qgraph     |
| Quantum Mechanics and Machine Learning Synergies: Graph Attention Neural Networks to Predict Chemical Reactivity            |   2022 | Machine Learning and Deep Learning                                                            | Mohammadamin TavakoliAaron MoodDavid Van VrankenPierre Baldi                                                                                                                                                                                                                                                                                                                                                                                                                                                | https://pubs.acs.org/doi/abs/10.1021/acs.jcim.1c01400                                                                       | Qgraph     |
| QuEst: Graph Transformer for Quantum Circuit Reliability Estimation                                                         |   2022 | arxiv                                                                                         | Hanrui Wang, Pengyu Liu, Jinglei Cheng, Zhiding Liang, Jiaqi Gu, Zirui Li, Yongshan Ding, Weiwen Jiang, Yiyu Shi, Xuehai Qian, David Z. Pan, Frederic T. Chong, Song Han                                                                                                                                                                                                                                                                                                                                    | https://arxiv.org/abs/2210.16724                                                                                            | Qgraph     |
| Novel Architecture of Parameterized Quantum Circuit for Graph Convolutional Network                                         |   2022 | arxiv                                                                                         | Yanhu Chen, Cen Wang, Hongxiang Guo, Jianwu                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | https://arxiv.org/abs/2203.03251                                                                                            | Qgraph     |
| Towards a Native Quantum Paradigm for Graph Representation Learning: A Sampling-based Recurrent Embedding Approach          |   2022 | KDD '22: Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining | Ge Yan, Yehui Tang, Junchi Yan                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | https://dl.acm.org/doi/abs/10.1145/3534678.3539327                                                                          | Qgraph     |
| QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks                                            |   2022 | arxiv                                                                                         | Kaixiong Zhou, Zhenyu Zhang, Shengyuan Chen, Tianlong Chen, Xiao Huang, Zhangyang Wang, Xia Hu                                                                                                                                                                                                                                                                                                                                                                                                              | https://arxiv.org/abs/2211.07379                                                                                            | Qgraph     |
| Qubit Routing Using Graph Neural Network Aided Monte Carlo Tree Search                                                      |   2022 | AAAI Technical Track on Planning, Routing, and Scheduling                                     | Animesh Sinha                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               | https://ojs.aaai.org/index.php/AAAI/article/view/21231                                                                      | Qgraph     |

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## 🔗 Cross-References
- [Quantum Computing Fundamentals](https://github.com/Q-brain/awesome-QAI-Papers-QComputing)  
- [Quantum Machine Learning](https://github.com/Q-brain/awesome-QAI-Papers-QML)  
- [Quantum Neural Networks and Quantum Recurrent Neural Networks](https://github.com/Q-brain/awesome-QAI-Papers-QNN-QRNN)  
- [Quantum Convolutional Neural Networks](https://github.com/Q-brain/awesome-QAI-Papers-QCNN)  
- [Quantum Reinforcement Learning](https://github.com/Q-brain/awesome-QAI-Papers-QRL)  
- [Quantum Generative Models](https://github.com/Q-brain/awesome-QAI-Papers-QGenerative)  
- [Quantum Diffusion Models](https://github.com/Q-brain/awesome-QAI-Papers-QDiffusion)  
- [Quantum Graph Learning](https://github.com/Q-brain/awesome-QAI-Papers-QGraph)  
- [Quantum Natural Language Processing](https://github.com/Q-brain/awesome-QAI-Papers-QText)  
- [Quantum Transfer Learning](https://github.com/Q-brain/awesome-QAI-Papers-QTL)

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## 🤝 Contributions
Contributions are welcome! Please ensure that new entries include:
1. Correct metadata (title, year, authors, publisher, link)  
2. Category tag (`QGraph`)  
3. Optional short summary of the contribution

---

## Authors and contributors

- [Ali Akbar Kiaei](https://github.com/a-kiaei) — repository engineering,
  automation, metadata tooling, CI, and release management
- [Mahnaz Bush](https://github.com/Mahnaz-Bush) — systematic literature
  review, paper screening, scientific taxonomy, curation, and documentation
- [Raha Aghaei](https://github.com/raha-aghaei-ai) — bibliographic validation,
  metadata quality assurance, duplicate detection, link verification, and
  reproducibility

## QAI-brain Research Collection

This repository is part of the [QAI-brain](https://github.com/QAI-brain) open research and software collection. Browse the [central Quantum AI paper index](https://github.com/QAI-brain/QAI-Papers) for related topics and repositories.

awesome-QAI-Papers-QGraph

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