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The k-nearest neighbors (k-NN) is a basic machine learning (ML) algorithm,and several quantum versions of it, employing different distance metrics, havebeen presented in the last few years. Although the Euclidean distance is one ofthe most widely used distance metrics in ML, it has not received muchconsideration in the development of these quantum variants. In this article, anovel quantum k-NN algorithm based on the Euclidean distance is introduced.Specifically, the algorithm is characterised by a quantum encoding requiring alow number of qubits and a simple quantum circuit not involving oracles,aspects that favor its realization. In addition to the mathematical formulationand some complexity observations, a detailed empirical evaluation withsimulations is presented. In particular, the results have shown the correctnessof the formulation, a drop in the performance of the algorithm when the numberof measurements is limited, the competitiveness with respect to some classicalbaseline methods in the ideal case, and the possibility of improving theperformance by increasing the number of measurements.

A quantum k-nearest neighbors algorithm based on the Euclidean distance estimation