  Dark Energy Spectroscopic Instrument (DESI) will construct a large and
precise three-dimensional map of our Universe. The survey effective volume
reaches $\sim20\Gpchcube$. It is a great challenge to prepare high-resolution
simulations with a much larger volume for validating the DESI analysis
pipelines. \textsc{AbacusSummit} is a suite of high-resolution dark-matter-only
simulations designed for this purpose, with $200\Gpchcube$ (10 times DESI
volume) for the base cosmology. However, further efforts need to be done to
provide a more precise analysis of the data and to cover also other
cosmologies. Recently, the CARPool method was proposed to use paired accurate
and approximate simulations to achieve high statistical precision with a
limited number of high-resolution simulations. Relying on this technique, we
propose to use fast quasi-$N$-body solvers combined with accurate simulations
to produce accurate summary statistics. This enables us to obtain 100 times
smaller variance than the expected DESI statistical variance at the scales we
are interested in, e.g. $k < 0.3\hMpc$ for the halo power spectrum. In
addition, it can significantly suppress the sample variance of the halo
bispectrum. We further generalize the method for other cosmologies with only
one realization in \textsc{AbacusSummit} suite to extend the effective volume
$\sim 20$ times. In summary, our proposed strategy of combining high-fidelity
simulations with fast approximate gravity solvers and a series of variance
suppression techniques sets the path for a robust cosmological analysis of
galaxy survey data.
