Optimization problems are fundamental in a wide range of fields, including telecommunications, where efficient resource allocation is critical to ensure good network performance and high scalability. In the context of elastic optical networks (EONs), the multi-objective routing and spectrum assignment (MO-RSA) problem represents a key challenge, as it involves selecting a valid path and assigning frequency slots while fulfilling continuity and contiguity constraints and optimizing multiple conflicting objectives. This paper presents a novel, to the best of our knowledge, quantum-based approach to solving the MO-RSA problem. We first formulate the MO-RSA problem as a quadratic unconstrained binary optimization (QUBO) problem and then solve it using the quantum approximate optimization algorithm (QAOA). Our method accounts for both minimizing the total number of used links (or any non-negative additive metric) and maximizing the optical signal-to-noise ratio. For our simulations, we employed the Qiskit framework and IBM’s sampler-based quantum backend to implement and test the proposed approach. Our results demonstrate that by encoding the MO-RSA problem into a QUBO model and optimizing it with QAOA, we achieved an approximation ratio of 88% and a computational complexity of O ( n 2 ) , which represents a significant improvement over the exponential complexity of traditional integer linear programming methods.