Systematic Effects in Interferometric Observations of the CMB
  Polarization
  The detection of the primordial $B$-mode spectrum of the polarized cosmic
microwave background (CMB) signal may provide a probe of inflation. However,
observation of such a faint signal requires excellent control of systematic
errors. Interferometry proves to be a promising approach for overcoming such a
challenge. In this paper we present a complete simulation pipeline of
interferometric observations of CMB polarization, including systematic errors.
We employ two different methods for obtaining the power spectra from mock data
produced by simulated observations: the maximum likelihood method and the
method of Gibbs sampling. We show that the results from both methods are
consistent with each other, as well as, within a factor of 6, with analytical
estimates. Several categories of systematic errors are considered: instrumental
errors, consisting of antenna gain and antenna coupling errors, and beam
errors, consisting of antenna pointing errors, beam cross-polarization and beam
shape (and size) errors. In order to recover the tensor-to-scalar ratio, $r$,
within a 10% tolerance level, which ensures the experiment is sensitive enough
to detect the $B$-signal at $r=0.01$ in the multipole range $28 < \ell < 384$,
we find that, for a QUBIC-like experiment, Gaussian-distributed systematic
errors must be controlled with precisions of $|g_{rms}| = 0.1$ for antenna
gain, $|\epsilon_{rms}| = 5 \times 10^{-4}$ for antenna coupling, $\delta_{rms}
\approx 0.7^\circ$ for pointing, $\zeta_{rms} \approx 0.7^\circ$ for beam
shape, and $\mu_{rms} = 5 \times 10^{-4}$ for beam cross-polarization.
