  We investigate the galaxy overdensity around proto-cluster scale quasar pairs
at high (z>3) and low (z~1) redshift based on the unprecedentedly wide and deep
optical survey of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP).
Using the first-year survey data covering effectively ~121 deg^2 with the
5sigma depth of i~26.4 and the SDSS DR12Q catalog, we find two luminous pairs
at z~3.3 and 3.6 which reside in >5sigma overdense regions of g-dropout
galaxies at i<25. The projected separations of the two pairs are R_perp=1.75
and 1.04 proper Mpc, and their velocity offsets are Delta V=692 and 1448 km
s^{-1}, respectively. This result is in clear contrast to the average z~4
quasar environments as discussed in Uchiyama et al. (2017) and implies that the
quasar activities of the pair members are triggered via major mergers in
proto-clusters, unlike the vast majority of isolated quasars in general fields
that may turn on via non-merger events such as bar and disk instabilities. At
z~1, we find 37 pairs with R_perp<2 pMpc and Delta V<2300 km s^{-1} in the
current HSC-Wide coverage, including four from Hennawi et al. (2006). The
distribution of the peak overdensity significance within two arcminutes around
the pairs has a long tail toward high density (>4sigma) regions. Thanks to the
large sample size, we find a statistical evidence that this excess is unique to
the pair environments when compared to single quasar and randomly selected
galaxy environments at the same redshift range. Moreover, there are nine
small-scale (R_perp<1 pMpc) pairs, two of which are found to reside in cluster
fields. Our results demonstrate that <2 pMpc-scale quasar pairs at both
redshift range tend to occur in massive haloes, although perhaps not the most
massive ones, and that they are useful to search for rare density peaks.
