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