Quantum mechanics emerge as a promise for the future of computing, broadening the horizons for solutions concerning complex tasks, e.g., NP-hard problems. Alongside quantum computing, machine learning has become indispensable. This paper explores the potential integration of quantum computing principles into the Optimum-Path Forest (OPF), a graph-based framework comprised of solutions for machine learning, optimization, and image processing. We are particularly interested in the supervised OPF approach, which elects the most representative samples for each class, aka prototypes, as the connected samples from different classes in a minimum spanning tree (MST) computed over the training set. By harnessing quantum parallelism and superposition, this paper introduces a new approach to identifying prototypes employing a quantum-based Traveler Salesman Problem (TSP) algorithm, which provides an alternative to computing MSTs and yields a hybrid version of the OPF classifier. The experiments on established datasets demonstrated the promising potential of this approach while also underscoring the necessity for further research in this field.