Euclid Quick Data Release (Q1): XVI. Optical and near-infrared identification and classification of point-like X-ray selected sources

To better understand the role of active galactic nuclei (AGN) in galaxy evolution, it is crucial to work with a complete and pure AGN sample. X-ray surveys are key to doing so, but their larger positional uncertainties complicate counterpart (CTP) association, further compounded by the limited availability of deep, uniform multi-wavelength ancillary data. Euclid is revolutionising this identification effort, offering extensive coverage of nearly the entire extragalactic sky, particularly in the near-infrared bands, where AGN are more easily detected. Using the first Euclid Quick Data Release (Q1), we validated the methods for identifying and classifying Euclid CTPs of known point-like sources from major X-ray surveys, including XMM-Newton, Chandra, and eROSITA. Using Bayesian statistics, combined with machine learning (ML), as incorporated in the algorithm NWAY, we identified the CTPs of 11 286 X-ray sources from the three X-ray telescopes. For the large majority of 10 194 sources, the association is unique, with the remaining ∼10% of multi-CTP cases equally split between XMM-Newton and eROSITA. Six percent of the Euclid CTPs are detected in more than one X-ray survey. We then used ML to distinguish between Galactic (8%) and extragalactic (92%) sources. We computed photo-zs using deep learning for the 9259 sources detected in the tenth data release of the DESI Legacy Survey, reaching an accuracy and a fraction of outliers of roughly 5%. Based on their X-ray luminosities, all CTPs identified as extragalactic are classified as AGN, most of which appear as type I AGN according to their hardness ratios. With this paper, we release our catalogue, which includes identifiers, basic X-ray properties, the reliability of the associations, and additional property extensions, such as Galactic- or extragalactic classifications and photometric/spectroscopic redshifts. We also provide probabilities for sub-selecting the sample based on purity and completeness, in order to allow users to tailor the sample according to their specific needs.