  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.
