Despite the great current relevance of Artificial Intelligence, and the extraordinary innovations that this discipline has brought to many fields -among which, without a doubt, medicine is found-, experts in medical applications of Artificial Intelligence are looking for new alternatives to solve problems for which current Artificial Intelligence programs do not provide with optimal solutions. For this, one promising option could be the use of the concepts and ideas of Quantum Mechanics, for the construction of quantum-based Artificial Intelligence systems. From a hybrid classical-quantum perspective, this article deals with the application of quantum computing techniques for the staging of Invasive Ductal Carcinoma of the breast. It includes: (1) a general explanation of a classical, and well-established, approach for medical reasoning, (2) a description of the clinical problem, (3) a conceptual model for staging invasive ductal carcinoma, (4) some basic notions about Quantum Rule-Based Systems, (5) a step-by-step explanation of the proposed approach for quantum staging of the invasive ductal carcinoma, and (6) the results obtained after running the quantum system on a significant number of use cases. A detailed discussion is also provided at the end of this paper.