  We carry out a comparative analysis of the relation between the mass of
supermassive black holes (BHs) and the stellar mass of their host galaxies at
$0.2<z<1.7$ using well-matched observations and multiple state-of-the-art
simulations (e.g., Massive Black II, Horizon-AGN, Illustris, TNG and a
semi-analytic model). The observed sample consists of 646 uniformly-selected
SDSS quasars ($0.2 < z < 0.8$) and 32 broad-line active galactic nuclei (AGNs;
$1.2<z<1.7$) with imaging from Hyper Suprime-Cam (HSC) for the former and
Hubble Space Telescope (HST) for the latter. We first add realistic
observational uncertainties to the simulation data and then construct a
simulated sample in the same manner as the observations. Over the full redshift
range, our analysis demonstrates that all simulations predict a level of
intrinsic scatter of the scaling relations comparable to the observations which
appear to agree with the dispersion of the local relation. Regarding the mean
relation, Horizon-AGN and TNG are in closest agreement with the observations at
low and high redshift ($z\sim$ 0.2 and 1.5, respectively) while the other
simulations show subtle differences within the uncertainties. For insight into
the physics involved, the scatter of the scaling relation, seen in the SAM, is
reduced by a factor of two and closer to the observations after adopting a new
feedback model that considers the geometry of the AGN outflow. The consistency
in the dispersion with redshift in our analysis supports the importance of both
quasar- and radio-mode feedback prescriptions in the simulations. Finally, we
highlight the importance of increasing the sensitivity (e.g., using the James
Webb Space Telescope), thereby pushing to lower masses and minimizing biases
due to selection effects.
