Particle track reconstruction plays a crucial role in the exploration of new physical phenomena,
particularly when rare signal tracks are obscured by a significant background. In muon colliders
where beam muons interacting with the detector produce secondary and tertiary background par-
ticles, track reconstruction can be computationally intensive due to the large number of detector
hits. The formulation of the reconstruction task as quadratic unconstrained binary optimisation
(QUBO) enables the use of quantum computers, which are believed to offer an advantage over
classical computers in such optimisation scenarios. The QUBO parameters are determined by
combining spatial and temporal information from detector hits, resulting in a 4D quantum al-
gorithm. To demonstrate the effectiveness of this approach, the quantum algorithm is used to
reconstruct signal tracks from samples consisting of Monte Carlo simulated charged particles
overlaid with background hits for a Muon Collider tracking detector. We will present the obtained
reconstruction performance and discuss possible paths for further improvements.