  The size of the dust torus in Active Galactic Nuclei (AGN) and their
high-luminosity counterparts, quasars, can be inferred from the time delay
between UV/optical accretion disk continuum variability and the response in the
mid-infrared (MIR) torus emission. This dust reverberation mapping (RM)
technique has been successfully applied to $\sim 70$ $z\lesssim 0.3$ AGN and
quasars. Here we present first results of our dust RM program for distant
quasars covered in the SDSS Stripe 82 region combining $\sim 20$-yr
ground-based optical light curves with 10-yr MIR light curves from the WISE
satellite. We measure a high-fidelity lag between W1-band (3.4 $\mu$m) and $g$
band for 587 quasars over $0.3\lesssim z\lesssim 2$ ($\left<z\right>\sim 0.8$)
and two orders of magnitude in quasar luminosity. They tightly follow
(intrinsic scatter $\sim 0.17$ dex in lag) the IR lag-luminosity relation
observed for $z<0.3$ AGN, revealing a remarkable size-luminosity relation for
the dust torus over more than four decades in AGN luminosity, with little
dependence on additional quasar properties such as Eddington ratio and
variability amplitude. This study motivates further investigations in the
utility of dust RM for cosmology, and strongly endorses a compelling science
case for the combined 10-yr Vera C. Rubin Observatory Legacy Survey of Space
and Time (optical) and 5-yr Nancy Grace Roman Space Telescope 2$\mu$m light
curves in a deep survey for low-redshift AGN dust RM with much lower
luminosities and shorter, measurable IR lags. The compiled optical and MIR
light curves for 7,384 quasars in our parent sample are made public with this
work.
