  We present a derivation of the star formation rate per comoving volume of
quasar host galaxies, derived from stacking analyses of far-infrared to mm-wave
photometry of quasars with redshifts 0<z<6 and absolute I-band magnitudes
-22>I_AB>-32. We use the science demonstration observations of the first ~16
deg^2 from the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS) in
which there are 240 quasars from the Sloan Digital Sky Survey (SDSS) and a
further 171 from the 2dF-SDSS LRG and QSO (2SLAQ) survey. We supplement this
data with a compilation of data from IRAS, ISO, Spitzer, SCUBA and MAMBO.
H-ATLAS alone statistically detects the quasars in its survey area at >5sigma
at 250, 350 and 500um. From the compilation as a whole we find striking
evidence of downsizing in quasar host galaxy formation: low-luminosity quasars
with absolute magnitudes in the range -22>I_AB>-24 have a comoving star
formation rate (derived from 100um rest-frame luminosities) peaking between
redshifts of 1 and 2, while high-luminosity quasars with I_AB<-26 have a
maximum contribution to the star formation density at z~3. The volume-averaged
star formation rate of -22>I_AB>-24 quasars evolves as (1+z)^{2.3 +/- 0.7} at
z<2, but the evolution at higher luminosities is much faster reaching (1+z)^{10
+/- 1} at -26>I_AB>-28. We tentatively interpret this as a combination of a
declining major merger rate with time and gas consumption reducing fuel for
both black hole accretion and star formation.
