  We carry out a search for strong-lens systems containing high-redshift lens
galaxies with the goal of extending strong-lensing-assisted galaxy evolutionary
studies to earlier cosmic time. Two strong-lens classifiers are constructed
from a deep residual network and trained with datasets of different
lens-redshift and brightness distributions. We classify a sample of 5,356,628
pre-selected objects from the Wide-layer fields in the second public data
release of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) by applying
the two classifiers to their HSC $gri$-filter cutouts. Cutting off at
thresholds that correspond to a false positive rate of $10^{-3}$ on our test
set, the two classifiers identify 5,468 and 6,119 strong-lens candidates.
Visually inspecting the cutouts of those candidates results in 735 grade-A or B
strong-lens candidates in total, of which 277 candidates are discovered for the
first time. This is the single largest set of galaxy-scale strong-lens
candidates discovered with HSC data to date, and nearly half of it (331/735)
contains lens galaxies with photometric redshifts above 0.6. Our discoveries
will serve as a valuable target list for ongoing and scheduled spectroscopic
surveys such as the Dark Energy Spectroscopic Instrument, the Subaru Prime
Focus Spectrograph project, and the Maunakea Spectroscopic Explorer.
