Powerful quasars can be seen out to large distances .
As they reside in massive dark matter haloes , they provide a useful tracer of large scale structure .
We stack Herschel -SPIRE images at 250 , 350 and 500 microns at the location of 11,235 quasars in ten redshift bins spanning 0.5 \leq z \leq 3.5 .
The unresolved dust emission of the quasar and its host galaxy dominate on instrumental beam scales , while extended emission is spatially resolved on physical scales of order a megaparsec .
This emission is due to dusty star-forming galaxies clustered around the dark matter haloes hosting quasars .
We measure radial surface brightness profiles of the stacked images to compute the angular correlation function of dusty star-forming galaxies correlated with quasars .
We then model the profiles to determine large scale clustering properties of quasars and dusty star-forming galaxies as a function of redshift .
We adopt a halo model and parameterize it by the most effective halo mass at hosting star-forming galaxies , finding \log ( M _ { \mathrm { eff } } / M _ { \odot } ) = 13.8 ^ { +0.1 } _ { -0.1 } at z = 2.21 - 2.32 , and , at z = 0.5 - 0.81 , the mass is \log ( M _ { \mathrm { eff } } / M _ { \odot } ) = 10.7 ^ { +1.0 } _ { -0.2 } .
Our results indicate a downsizing of dark matter haloes hosting dusty star-forming galaxies between 0.5 \leq z \la 2.9 .
The derived dark matter halo masses are consistent with other measurements of star-forming and sub-millimeter galaxies .
The physical properties of dusty star-forming galaxies inferred from the halo model depend on details of the quasar halo occupation distribution in ways that we explore at z > 2.5 , where the quasar HOD parameters are not well constrained .