The evolution of neutral gas in damped Lyman $\alpha$ systems from the
  XQ-100 survey
  We present a sample of 38 intervening Damped Lyman $\alpha$ (DLA) systems
identified towards 100 $z>3.5$ quasars, observed during the XQ-100 survey. The
XQ-100 DLA sample is combined with major DLA surveys in the literature. The
final combined sample consists of 742 DLAs over a redshift range approximately
$1.6 < z_{\rm abs} < 5.0$. We develop a novel technique for computing
$\Omega_{\rm HI}^{\rm DLA}$ as a continuous function of redshift, and we
thoroughly assess and quantify the sources of error therein, including fitting
errors and incomplete sampling of the high column density end of the column
density distribution function. There is a statistically significant redshift
evolution in $\Omega_{\rm HI}^{\rm DLA}$ ($\geq 3 \sigma$) from $z \sim 2$ to
$z \sim$ 5. In order to make a complete assessment of the redshift evolution of
$\Omega_{\rm HI}$, we combine our high redshift DLA sample with absorption
surveys at intermediate redshift and 21cm emission line surveys of the local
universe. Although $\Omega_{\rm HI}^{\rm DLA}$, and hence its redshift
evolution, remains uncertain in the intermediate redshift regime ($0.1 < z_{\rm
abs} < 1.6$), we find that the combination of high redshift data with 21cm
surveys of the local universe all yield a statistically significant evolution
in $\Omega_{\rm HI}$ from $z \sim 0$ to $z \sim 5$ ($\geq 3 \sigma$). Despite
its statistical significance, the magnitude of the evolution is small: a linear
regression fit between $\Omega_{\rm HI}$ and $z$ yields a typical slope of
$\sim$0.17$\times 10^{-3}$, corresponding to a factor of $\sim$ 4 decrease in
$\Omega_{\rm HI}$ between $z=5$ and $z=0$.
