The exponential growth of space debris in Low Earth Orbit (LEO) poses a significant challenge to the sustainability of space operations. Despite preventive measures aimed at limiting debris generation, they remain insufficient to address the increasing accumulation of defunct satellites, rocket stages, and collision fragments. Active Debris Removal (ADR) has emerged as a promising solution, particularly in multi-target missions, which require solving complex combinatorial optimization problems similar to the Traveling Salesman Problem (TSP) to maximize the efficiency of the missions, minimizing fuel use and mission duration. This thesis explores the application of Quantum Annealing (QA) and Hybrid Quantum Annealing (HQA) to optimize multi-target ADR missions.