  Large samples of high-redshift supernovae (SNe) are potentially powerful
probes of cosmic star formation, metal enrichment, and SN physics. We present
initial results from a new deep SN survey, based on re-imaging in the R, i', z'
bands, of the 0.25 deg2 Subaru Deep Field (SDF), with the 8.2-m Subaru
telescope and Suprime-Cam. In a single new epoch consisting of two nights of
observations, we have discovered 33 candidate SNe, down to a z'-band magnitude
of 26.3 (AB). We have measured the photometric redshifts of the SN host
galaxies, obtained Keck spectroscopic redshifts for 17 of the host galaxies,
and classified the SNe using the Bayesian photometric algorithm of Poznanski et
al. (2007) that relies on template matching. After correcting for biases in the
classification, 55% of our sample consists of Type Ia supernovae and 45% of
core-collapse SNe. The redshift distribution of the SNe Ia reaches z ~ 1.6,
with a median of z ~ 1.2. The core-collapse SNe reach z ~ 1.0, with a median of
z ~ 0.5. Our SN sample is comparable to the Hubble Space Telescope/GOODS sample
both in size and redshift range. The redshift distributions of the SNe in the
SDF and in GOODS are consistent, but there is a trend (which requires
confirmation using a larger sample) for more high-z SNe Ia in the SDF. This
trend is also apparent when comparing the SN Ia rates we derive to those based
on GOODS data. Our results suggest a fairly constant rate at high redshift that
could be tracking the star-formation rate. Additional epochs on this field,
already being obtained, will enlarge our SN sample to the hundreds, and
determine whether or not there is a decline in the SN Ia rate at z >~ 1.
