  The 2-m aperture Chinese Space Station Telescope (CSST), which observes at
wavelengths ranging from 255 to 1000 nm, is expected to start science
operations in 2024. An ultra-deep field observation program covering
approximately 10 square degrees is proposed with supernovae (SNe) and other
transients as one of its primary science drivers. This paper presents the
simulated detection results of type Ia supernovae (SNe Ia) and explores the
impact of new datasets on the determinations of cosmological parameters. The
simulated observations are conducted with an exposure time of 150 s and
cadences of 10, 20, and 30 days. The survey mode covering a total of 80
observations but with a random cadence in the range of 4 to 14 days is also
explored. Our simulation results indicate that the CSST can detect up to $\sim
1800$ SNe Ia at z $<$ 1.3. The simulated SNe Ia are then used to constrain the
cosmological parameters. The constraint on $\Omega_m$ can be improved by 37.5%
using the 10-day cadence sample in comparison with the Pantheon sample. A
deeper measurement simulation with a 300 s exposure time together with the
Pantheon sample improves the current constraints on $\Omega_m$ by 58.3% and
$\omega$ by 47.7%. Taking future ground-based SNe Ia surveys into
consideration, the constraints on $\omega$ can be improved by 59.1%. The CSST
ultra-deep field observation program is expected to discover large amounts of
SNe Ia over a broad redshift span and enhance our understanding of the nature
of dark energy.
