Comparative study of quantum methods in the resolution of track findings instances

Track finding can be considered as a complex optimization problem initially introduced in particle physics involving the reconstruction of particle trajectories. A track is typically composed of several consecutive segments (track segments) that resembles a smooth curve without bifurcations. In this paper various modeling approaches are explored in order to assess both their impact and their effectiveness in solving them using quantum and classical methods. We present implementations of three classical models using CPLEX, two quantum models running on actual D-Wave quantum computers, and one quantum model on a D-Wave simulator. To facilitate a fair comparative study and encourage future research in this area, we introduce a new set of benchmark instances, categorized into small, medium, and large scales. Our evaluation of these methods on the benchmark instances indicates that D-Wave methods offer an excellent balance between computation time and result quality, outperforming CPLEX in numerous cases.