  The relationship between quasars and their host galaxies provides clues on
how supermassive black holes (SMBHs) and massive galaxies are jointly
assembled. To elucidate this connection, we measure the structural and
photometric properties of the host galaxies of ~5000 SDSS quasars at 0.2<z<1
using five-band (grizy) optical imaging from the Hyper Suprime-Cam Subaru
Strategic Program. An automated analysis tool is used to forward-model the
blended emission of the quasar as characterized by the point spread function
and the underlying host galaxy as a two-dimensional Sersic profile. In
agreement with previous studies, quasars are preferentially hosted by massive
star-forming galaxies with disk-like light profiles. Furthermore, we find that
the size distribution of quasar hosts is broad at a given stellar mass and the
average values exhibit a size-stellar mass relation as seen with inactive
galaxies. In contrast, the sizes of quasar hosts are more compact than inactive
star-forming galaxies on average, but not as compact as quiescent galaxies of
similar stellar masses. This is true irrespective of quasar properties
including bolometric luminosity, Eddington ratio, and black hole mass. These
results are consistent with a scenario in which galaxies are concurrently
fueling a SMBH and building their stellar bulge from a centrally-concentrated
gas reservoir. Alternatively, quasar hosts may be experiencing a compaction
process in which stars from the disk and inflowing gas are responsible for
growing the bulge. In addition, we confirm that the host galaxies of type-1
quasars have a bias of being closer towards face-on, suggesting that
galactic-scale dust can contribute to obscuring the broad-line region.
