LUXE (Laser Und XFEL Experiment) is a proposed experiment at DESY using the electron beam of the European XFEL and a high-intensity laser. LUXE will study Quantum Electrodynamics (QED) in the strong-field regime, where QED becomes non-perturbative. One of the key measurements is the positron rate from electron-positron pair creation, which is enabled by the use of a silicon tracking detector. Precision tracking of positrons becomes very challenging at high laser intensities due to the high rates, which can be computationally expensive for classical computers. I will present the overall status of the LUXE experiment and focus on the study of quantum algorithm-based tracking. The results will be discussed in comparison with state-of-the-art classical methods using Graph Neural Networks or a Combinatorial Kalman Filter.