# Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction

arXiv: https://arxiv.org/abs/2109.12636 · HTML: https://mlsanity.com/paper/2109.12636/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 71 references that are in the map.
- First posted on arXiv 26 Sep 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [MLPF: Efficient machine-learned particle-flow reconstruction using graph neural networks](https://mlsanity.com/paper/2101.08578/) (2021)
- [Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus](https://mlsanity.com/paper/2102.01828/) (2021)
- [Hybrid Quantum-Classical Graph Convolutional Network](https://mlsanity.com/paper/2101.06189/) (2021)
- [Matrix Product State Based Quantum Classifier](https://mlsanity.com/paper/1905.01426/) (2019)
- [The Tracking Machine Learning challenge : Throughput phase](https://mlsanity.com/paper/2105.01160/) (2021)
- [Dual-Parameterized Quantum Circuit GAN Model in High Energy Physics](https://mlsanity.com/paper/2103.15470/) (2021)
- [Training Saturation in Layerwise Quantum Approximate Optimisation](https://mlsanity.com/paper/2106.13814/) (2021)

## Built on by (most cited first, 20 of 20)

- [Financial Fraud Detection using Quantum Graph Neural Networks](https://mlsanity.com/paper/2309.01127/) (2023)
- [Quantum anomaly detection in the latent space of proton collision events at the LHC](https://mlsanity.com/paper/2301.10780/) (2023)
- [Towards Quantum Graph Neural Networks: An Ego-Graph Learning Approach](https://mlsanity.com/paper/2201.05158/) (2022)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Quantum Graph Learning: Frontiers and Outlook](https://mlsanity.com/paper/2302.00892/) (2023)
- [From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks](https://mlsanity.com/paper/2408.06524/) (2024)
- [Equivariance Is Not All You Need: Characterizing the Utility of Equivariant Graph Neural Networks for Particle Physics Tasks](https://mlsanity.com/paper/2311.03094/) (2023)
- [From Quantum Graph Computing to Quantum Graph Learning: A Survey](https://mlsanity.com/paper/2202.09506/) (2022)
- [A hybrid quantum-classical fusion neural network to improve protein-ligand binding affinity predictions for drug discovery](https://mlsanity.com/paper/2309.03919/) (2023)
- [Graph Neural Networks on Quantum Computers](https://mlsanity.com/paper/2405.17060/) (2024)
- [Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries](https://mlsanity.com/paper/2409.15645/) (2024)
- [Optimizing Quantum Convolutional Neural Network Architectures for Arbitrary Data Dimension](https://mlsanity.com/paper/2403.19099/) (2024)
- [A unifying primary framework for quantum graph neural networks from quantum graph states](https://mlsanity.com/paper/2402.13001/) (2024)
- [Inductive Graph Representation Learning with Quantum Graph Neural Networks](https://mlsanity.com/paper/2503.24111/) (2025)
- [Hybrid Quantum Neural Networks for Efficient Protein-Ligand Binding Affinity Prediction](https://mlsanity.com/paper/2509.11046/) (2025)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Guided Graph Compression for Quantum Graph Neural Networks](https://mlsanity.com/paper/2506.09862/) (2025)
- [Variational Quantum Algorithms for Particle Track Reconstruction](https://mlsanity.com/paper/2511.11397/) (2025)
- [Edge-Local and Qubit-Efficient Quantum Graph Learning for the NISQ Era](https://mlsanity.com/paper/2602.16018/) (2026)
- [Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables](https://mlsanity.com/paper/2605.13383/) (2026)

## Abstract (arXiv)

The Large Hadron Collider (LHC) at the European Organisation for Nuclear Research (CERN) will be upgraded to further increase the instantaneous rate of particle collisions (luminosity) and become the High Luminosity LHC (HL-LHC). This increase in luminosity will significantly increase the number of particles interacting with the detector. The interaction of particles with a detector is referred to as "hit". The HL-LHC will yield many more detector hits, which will pose a combinatorial challenge by using reconstruction algorithms to determine particle trajectories from those hits. This work explores the possibility of converting a novel Graph Neural Network model, that can optimally take into account the sparse nature of the tracking detector data and their complex geometry, to a Hybrid Quantum-Classical Graph Neural Network that benefits from using Variational Quantum layers. We show that this hybrid model can perform similar to the classical approach. Also, we explore Parametrized Quantum Circuits (PQC) with different expressibility and entangling capacities, and compare their training performance in order to quantify the expected benefits. These results can be used to build a future road map to further develop circuit based Hybrid Quantum-Classical Graph Neural Networks.