We present Institut de Radioastronomie Millimétrique Plateau de Bure Interferometer observations of the ^(12)CO (3–2) emission from two far-infrared luminous QSOs at z ∼ 2.5 selected from the Herschel-Astrophysical Tetrahertz Large Area Survey. These far-infrared bright QSOs were selected to have supermassive black holes (SMBHs) with masses similar to those thought to reside in submillimetre galaxies (SMGs) at z ∼ 2.5, making them ideal candidates as systems in the potential transition from an ultraluminous infrared galaxy phase to a submillimetre faint, unobscured, QSO. We detect ^(12)CO (3–2) emission from both QSOs and we compare their baryonic, dynamical and SMBH masses to those of SMGs at the same epoch. We find that these far-infrared bright QSOs have similar dynamical but lower gas masses than SMGs. We combine our results with literature values and find that at a fixed LFIR, far-infrared bright QSOs have ∼50 ± 30 per cent less warm/dense gas than SMGs. Taken together with previous results, which show that QSOs lack the extended, cool reservoir of gas seen in SMGs, this suggests that far-infrared bright QSOs are at a different evolutionary stage. This is consistent with the hypothesis that far-infrared bright QSOs represent a short (∼1 Myr) but ubiquitous phase in the transformation of dust-obscured, gas-rich, starburst-dominated SMGs into unobscured, gas-poor, QSOs
