The High Luminosity Large Hadron Collider (HL-LHC) at CERN will involve a significant increase in the complexity and sheer size of data with respect to the current LHC experimental complex. Hence, the task of reconstructing the particle trajectories will become more and more complex due to the number of simultaneous collisions and the resulting increased detector occupancy. Aiming to identify the particle paths, machine learning techniques such as graph neural networks are being explored in the HEP.TrkX project and its successor, the Exa.TrkX project. Both show promising results and reduce the combinatorial nature of the problem. Previous results of our team have demonstrated the successful attempt of including quantum computing concepts within graph neural networks that are able to reconstruct the particle track based on the hits of the detector. A higher overall accuracy is gained by representing the training data in a meaningful way within an embedded space. That has been included in the Exa.TrkX project by applying a classical MLP. Consequently, pairs of hits belonging to different trajectories are pushed apart while those belonging to the same ones stay close together. We explore the applicability of quantum circuits within the task of embedding using hybrid-classical neural network architectures and show preliminary results.