Estimating the completeness of the QUBRICS survey with 3501 quasi-stellar object redshifts from Gaia DR3 spectra

Quasi-stellar objects (QSOs) are essential for investigating the structure and evolution of the Universe. Historically, their identification has been concentrated in the northern hemisphere, primarily due to the sky coverage of major astronomical surveys. The QUBRICS (QUasars as BRIght beacons for Cosmology in the Southern hemisphere) survey, started in 2019 to address this asymmetry, has identified more than 1300 new bright (i<19.5) high-redshift (2.5<z<6) QSOs in the southern sky. This study aims to quantify, using an independent QSO sample, the completeness and recall of the QUBRICS QSO selection methods, based on extreme gradient boosting (XGB) and probabilistic random forest (PRF) techniques, since completeness is a fundamental metric for ensuring the statistical robustness of QSO-based cosmological investigations. We analyzed a subset of DR3 sources (G<18.25, $|b|>25$ deg, negligible parallax and proper motion) with low-resolution spectra, from which we obtained a sample of 3501 QSOs. To determine how many QSOs were correctly identified as candidates, we crossmatched this independent sample with the datasets used for selection: 894 QSOs with z>2.5 fell within the XGB dataset footprint, of which 152 were unclassified and thus eligible for completeness testing. Similarly, 675 QSOs with z>2.5 were within the PRF dataset footprint, including 69 unclassified objects. Gaia The XGB correctly identified as candidates 136 (89%) of the 152 QSOs with z>2.5 listed in the XGB dataset as unclassified objects. The PRF correctly identified as candidates 46 (66%) of the 69 QSOs with z>2.5 listed in the PRF dataset as unclassified objects. These findings confirm the high efficiency of the QUBRICS selection methods (recall $=89%$) and provide the completeness estimate for spectroscopically confirmed QSOs (82%), which is necessary for cosmological studies that use QUBRICS data. This work also provides reliable redshifts for 1223 new QSOs (median redshift z=2.1 and magnitude G=17.8), which will help improve the performance of future selections.