  Unprecedented increase of complexity and scale of data is expected in
computation necessary for the tracking detectors of the High Luminosity Large
Hadron Collider (HL-LHC) experiments. While currently used Kalman filter based
algorithms are reaching their limits in terms of ambiguities from increasing
number of simultaneous collisions, occupancy, and scalability (worse than
quadratic), a variety of machine learning approaches to particle track
reconstruction are explored. It has been demonstrated previously by HEP.TrkX
using TrackML datasets, that graph neural networks, by processing events as a
graph connecting track measurements can provide a promising solution by
reducing the combinatorial background to a manageable amount and are scaling to
a computationally reasonable size. In previous work, we have shown a first
attempt of Quantum Computing to Graph Neural Networks for track reconstruction
of particles. We aim to leverage the capability of quantum computing to
evaluate a very large number of states simultaneously and thus to effectively
search a large parameter space. As the next step in this paper, we present an
improved model with an iterative approach to overcome the low accuracy
convergence of the initial oversimplified Tree Tensor Network (TTN) model.
