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ABSTRACT With the launch of eROSITA (extended Roentgen Survey with an Imaging Telescope Array), successfully occurred on 2019 July 13, we are facing the challenge of computing reliable photometric redshifts for 3 million of active galactic nuclei (AGNs) over the entire sky, having available only patchy and inhomogeneous ancillary data. While we have a good understanding of the photo-z quality obtainable for AGN using spectral energy distribution (SED)-fitting technique, we tested the capability of machine learning (ML), usually reliable in computing photo-z for QSO in wide and shallow areas with rich spectroscopic samples. Using MLPQNA as example of ML, we computed photo-z for the X-ray-selected sources in Stripe 82X, using the publicly available photometric and spectroscopic catalogues. Stripe 82X is at least as deep as eROSITA will be and wide enough to include also rare and bright AGNs. In addition, the availability of ancillary data mimics what can be available in the whole sky. We found that when optical, and near- and mid-infrared data are available, ML and SED fitting perform comparably well in terms of overall accuracy, realistic redshift probability density functions, and fraction of outliers, although they are not the same for the two methods. The results could further improve if the photometry available is accurate and including morphological information. Assuming that we can gather sufficient spectroscopy to build a representative training sample, with the current photometry coverage we can obtain reliable photo-z for a large fraction of sources in the Southern hemisphere well before the spectroscopic follow-up, thus timely enabling the eROSITA science return. The photo-z catalogue is released here. 

Context. In November 2019, eROSITA on board of the Spektrum-Roentgen-Gamma (SRG) observatory started to map the entire sky in X-rays. After the four-year survey program, it will reach a flux limit that is about 25 times deeper than ROSAT. During the SRG performance verification phase, eROSITA observed a contiguous 140 deg 2 area of the sky down to the final depth of the eROSITA all-sky survey (eROSITA Final Equatorial-Depth Survey; eFEDS), with the goal of obtaining a census of the X-ray emitting populations (stars, compact objects, galaxies, clusters of galaxies, and active galactic nuclei) that will be discovered over the entire sky. Aims. This paper presents the identification of the counterparts to the point sources detected in eFEDS in the main and hard samples and their multi-wavelength properties, including redshift. Methods. To identifyy the counterparts, we combined the results from two independent methods ( NWAY and ASTROMATCH ), trained on the multi-wavelength properties of a sample of 23k XMM-Newton sources detected in the DESI Legacy Imaging Survey DR8. Then spectroscopic redshifts and photometry from ancillary surveys were collated to compute photometric redshifts. Results. Of the eFEDS sources, 24 774 of 27 369 have reliable counterparts (90.5%) in the main sample and 231 of 246 sourcess (93.9%) have counterparts in the hard sample, including 2514 (3) sources for which a second counterpart is equally likely. By means of reliable spectra, Gaia parallaxes, and/or multi-wavelength properties, we have classified the reliable counterparts in both samples into Galactic (2695) and extragalactic sources (22 079). For about 340 of the extragalactic sources, we cannot rule out the possibility that they are unresolved clusters or belong to clusters. Inspection of the distributions of the X-ray sources in various optical/IR colour-magnitude spaces reveal a rich variety of diverse classes of objects. The photometric redshifts are most reliable within the KiDS/VIKING area, where deep near-infrared data are also available. Conclusions. This paper accompanies the eROSITA early data release of all the observations performed during the performance and verification phase. Together with the catalogues of primary and secondary counterparts to the main and hard samples of the eFEDS survey, this paper releases their multi-wavelength properties and redshifts.