  Pair-instability supernovae are theorized supernovae that have not yet been
observationally confirmed. They are predicted to exist in low-metallicity
environments. Because overall metallicity becomes lower at higher redshifts,
deep near-infrared transient surveys probing high-redshift supernovae are
suitable to discover pair-instability supernovae. The Euclid satellite, which
is planned to be launched in 2023, has a near-infrared wide-field instrument
that is suitable for a high-redshift supernova survey. The Euclid Deep Survey
is planned to make regular observations of three Euclid Deep Fields (40 deg2 in
total) spanning the Euclid's 6 year primary mission period. While the
observations of the Euclid Deep Fields are not frequent, we show that the
predicted long duration of pair-instability supernovae would allow us to search
for high-redshift pair-instability supernovae with the Euclid Deep Survey.
Based on the current observational plan of the Euclid mission, we conduct
survey simulations in order to estimate the expected numbers of
pair-instability supernova discoveries. We find that up to several hundred
pair-instability supernovae at z < ~ 3.5 can be discovered within the Euclid
Deep Survey. We also show that pair-instability supernova candidates can be
efficiently identified by their duration and color that can be determined with
the current Euclid Deep Survey plan. We conclude that the Euclid mission can
lead to the first confirmation of pair-instability supernovae if their event
rates are as high as those predicted by recent theoretical studies. We also
update the expected numbers of superluminous supernova discoveries in the
Euclid Deep Survey based on the latest observational plan.
