[Paper Review] Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction

Cenk Tüysüz, Carla Rieger+7 more|arXiv (Cornell University)|Sep 26, 2021

Quantum Computing Algorithms and Architecture76 references58 citations

TL;DR

This paper proposes a hybrid quantum-classical Graph Neural Network (QGNN) for particle track reconstruction in high-luminosity LHC experiments, leveraging variational quantum circuits to process sparse, geometric detector data. The QGNN achieves performance comparable to classical GNNs on the TrackML benchmark, with circuit 10 showing optimal training stability despite low expressibility, suggesting potential for quantum advantage with further optimization.

ABSTRACT

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.

Motivation & Objective

• Address the growing computational challenge of particle track reconstruction under high-luminosity LHC conditions, where classical algorithms scale poorly.
• Investigate whether hybrid quantum-classical Graph Neural Networks (QGNNs) can match or surpass classical GNNs in reconstructing particle trajectories from detector hits.
• Evaluate the impact of different Parametrized Quantum Circuit (PQC) architectures on training performance and model expressivity.
• Assess the feasibility of using NISQ-era quantum hardware for high-energy physics applications, particularly in track reconstruction.

Proposed method

• Implement a hybrid quantum-classical GNN model where quantum circuits process node and edge features in a graph-structured representation of detector hits.
• Use angle encoding to map classical particle hit data (position, momentum) into quantum states on 16 or fewer qubits.
• Apply variational quantum circuits (PQCs) with varying entangling capabilities and expressibility to encode geometric and topological relationships between hits.
• Train the model using a differentiable quantum machine learning framework (TensorFlow Quantum) with a graph attention mechanism to weight edge contributions.
• Optimize the model via stochastic gradient descent with 20 epochs maximum, using a pT-cut to reduce dataset size and computational load.
• Compare performance against a classical GNN baseline (HEP.TrkX) using the same preprocessed TrackML dataset and evaluation metrics.

Experimental results

Research questions

• RQ1 Can a hybrid quantum-classical Graph Neural Network achieve performance comparable to classical GNNs in particle track reconstruction on the TrackML dataset?
• RQ2 How do different PQC architectures—varying in expressibility and entangling capacity—affect training stability and convergence in the QGNN model?
• RQ3 Does the use of quantum circuits provide any advantage over classical neural networks in terms of model capacity or generalization for this task?
• RQ4 To what extent do noise effects and hardware limitations on current NISQ devices constrain the practical deployment of QGNNs in high-energy physics?

Key findings

• The hybrid QGNN model achieves validation loss performance comparable to the classical GNN baseline across all tested hidden dimension sizes, with no significant performance gap observed.
• Circuit 10, despite having the lowest expressibility and entangling capacity among tested PQCs, consistently outperformed other circuits in training stability and final loss, suggesting robustness over expressivity in this setup.
• Training times exceeded one week for models with 16 qubits due to high RAM and simulation overhead, limiting scalability and necessitating data reduction via pT-cut and qubit count reduction.
• The model's performance saturates with increasing hidden dimension size, indicating a plateau in learning capacity beyond a certain model depth.
• Simulations were restricted to 16 qubits due to classical hardware and simulation time constraints, preventing exploration of larger-scale quantum models.
• Noise effects were not fully explored due to technical limitations, though prior literature suggests potential noise resilience in variational quantum algorithms.