  We perform an ensemble of $N$-body simulations with $2048^3$ particles for
101 flat $w$CDM cosmological models sampled based on a maximin-distance Sliced
Latin Hypercube Design. By using the halo catalogs extracted at multiple
redshifts in the range of $z=[0,1.48]$, we develop Dark Emulator, which enables
fast and accurate computations of the halo mass function, halo-matter
cross-correlation, and halo auto-correlation as a function of halo masses,
redshift, separations and cosmological models, based on the Principal Component
Analysis and the Gaussian Process Regression for the large-dimensional input
and output data vector. We assess the performance of the emulator using a
validation set of $N$-body simulations that are not used in training the
emulator. We show that, for typical halos hosting CMASS galaxies in the Sloan
Digital Sky Survey, the emulator predicts the halo-matter cross correlation,
relevant for galaxy-galaxy weak lensing, with an accuracy better than $2\%$ and
the halo auto-correlation, relevant for galaxy clustering correlation, with an
accuracy better than $4\%$. We give several demonstrations of the emulator. It
can be used to study properties of halo mass density profiles such as the
mass-concentration relation and splashback radius for different cosmologies.
The emulator outputs can be combined with an analytical prescription of
halo-galaxy connection such as the halo occupation distribution at the equation
level, instead of using the mock catalogs, to make accurate predictions of
galaxy clustering statistics such as the galaxy-galaxy weak lensing and the
projected correlation function for any model within the $w$CDM cosmologies, in
a few CPU seconds.
