  Although Type Ia supernova cosmology has now reached a mature state, it is
important to develop as many independent methods as possible to understand the
true nature of dark energy. Recent studies have shown that Type II supernovae
(SNe II) offer such a path and could be used as alternative distance
indicators. However, the majority of these studies were unable to extend the
Hubble diagram above redshift $z=0.3$ because of observational limitations.
Here, we show that we are now ready to move beyond low redshifts and attempt
high-redshift ($z \gtrsim 0.3$) SN~II cosmology as a result of new-generation
deep surveys such as the Subaru/Hyper Suprime-Cam (HSC) survey. Applying the
"standard candle method" to SN$\sim$2016jhj ($z=0.3398 \pm 0.0002$; discovered
by HSC) together with a low-redshift sample, we are able to construct the
highest-redshift SN II Hubble diagram to date with an observed dispersion of
0.27 mag (i.e., 12-13% in distance). This work demonstrates the bright future
of SN~II cosmology in the coming era of large, wide-field surveys like that of
the Large Synoptic Survey Telescope.
