The type Ia supernova ( SN Ia ) rate , when compared to the cosmic star formation history ( SFH ) , can be used to derive the delay-time distribution ( DTD , the hypothetical SN Ia rate vs. time following a brief burst of star formation ) of SNe Ia , which can distinguish among progenitor models . We present the results of a SN survey in the Subaru Deep Field ( SDF ) . Over a period of three years , we have observed the SDF on four independent epochs with Suprime-Cam on the Subaru 8.2-m telescope , with two nights of exposure per epoch , in the R , i ^ { \prime } , and z ^ { \prime } bands . We have discovered 150 SNe out to redshift z \approx 2 . Using 11 photometric bands from the observer-frame far-ultraviolet to the near-infrared , we derive photometric redshifts for the SN host galaxies ( for 24 we also have spectroscopic redshifts ) . This information is combined with the SN photometry to determine the type and redshift distribution of the SN sample . Our final sample includes 28 SNe Ia in the range 1.0 < z < 1.5 and 10 in the range 1.5 < z < 2.0 . As our survey is largely insensitive to core-collapse SNe ( CC SNe ) at z > 1 , most of the events found in this range are likely SNe Ia . Our SN Ia rate measurements are consistent with those derived from the Hubble Space Telescope ( HST ) GOODS sample , but the overall uncertainty of our 1.5 < z < 2.0 measurement is a factor of 2 smaller , of 35–50 per cent . Based on this sample , we find that the SN Ia rate evolution levels off at 1.0 < z < 2.0 , but shows no sign of declining . Combining our SN Ia rate measurements and those from the literature , and comparing to a wide range of possible SFHs , the best-fitting DTD ( with a reduced \chi ^ { 2 } = 0.7 ) is a power law of the form \Psi ( t ) \propto t ^ { \beta } , with index \beta = -1.1 \pm 0.1 ( statistical ) \pm 0.17 ( systematic ) . This result is consistent with other recent DTD measurements at various redshifts and environments , and is in agreement with a generic prediction of the double-degenerate progenitor scenario for SNe Ia . Most single-degenerate models predict different DTDs . By combining the contribution from CC SNe , based on the wide range of SFHs , with that from SNe Ia , calculated with the best-fitting DTD , we predict that the mean present-day cosmic iron abundance is in the range Z _ { Fe } = ( 0.09 – 0.37 ) ~ { } Z _ { Fe, \odot } . We further predict that the high- z SN searches now beginning with HST will discover 2–11 SNe Ia at z > 2 .