The DESI $N$-body Simulation Project II: Suppressing Sample Variance
  with Fast Simulations
  Dark Energy Spectroscopic Instrument (DESI) will construct a large and
precise 3D map of our Universe. The survey effective volume reaches $\sim20$
Gpc$^3h^{-3}$. It is a great challenge to prepare high-resolution simulations
with a much larger volume for validating the DESI analysis pipelines.
AbacusSummit is a suite of high-resolution dark-matter-only simulations
designed for this purpose, with $200$ Gpc$^3h^{-3}$ (10 times DESI volume) for
the base cosmology. However, further efforts need to be done to provide 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 variances than the
expected DESI statistical variance at the scales we are interested in, e.g., $k
< 0.3~h$Mpc$^{-1}$. We further generalize the method for other cosmologies with
only one realization in 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.
