  The LUXE experiment (LASER Und XFEL Experiment) is a new experiment in
planning at DESY Hamburg, which will study Quantum Electrodynamics (QED) at the
strong-field frontier. In this regime, QED is non-perturbative. This manifests
itself in the creation of physical electron-positron pairs from the QED vacuum.
LUXE intends to measure the positron production rate in this unprecedented
regime by using, among others, a silicon tracking detector. The large number of
expected positrons traversing the sensitive detector layers results in an
extremely challenging combinatorial problem, which can become computationally
very hard for classical computers. This paper presents a preliminary study to
explore the potential of quantum computers to solve this problem and to
reconstruct the positron trajectories from the detector energy deposits. The
reconstruction problem is formulated in terms of a quadratic unconstrained
binary optimisation. Finally, the results from the quantum simulations are
discussed and compared with traditional classical track reconstruction
algorithms.
