<p>Quantum computing has become a breakthrough in many different research and applied areas. As various authors have demonstrated, the quantum properties have made some computational processes parallel and impossible to compute or even simulate for classical computers. An area that has been significantly impacted is machine learning. For instance, notable advances have been made in the field of classification and clustering, with computational complexity being reduced or with results being achieved that are, at least, equivalent to those classically obtained. In these problems, metric selection is critical. This paper proposes to compute the Hausdorff metric for the classification problem using quantum-based Euclidean distance. The Hausdorff metric has been shown to offer optimal results in various domains, including pattern recognition and image segmentation, making it a preferred metric in these applications. The presented algorithmic approach was applied to the Iris and Palmer Penguins datasets as input, with the classical k-neighbor nearest algorithm serving as the basis for classification. The quantitative results of this work demonstrate comparable evaluation metrics concerning the pure-classical k-neighbor-nearest algorithm.</p>