  The accurate description of electrons at extreme density and temperature is
of paramount importance for, e.g., the understanding of astrophysical objects
and inertial confinement fusion. In this context, the dynamic structure factor
$S(\mathbf{q},\omega)$ constitutes a key quantity as it is directly measured in
X-ray Thomson (XRTS) scattering experiments and governs transport properties
like the dynamic conductivity. In this work, we present the first \textit{ab
initio} results for $S(\mathbf{q},\omega)$ by carrying out extensive path
integral Monte Carlo simulations and developing a new method for the required
analytic continuation, which is based on the stochastic sampling of the dynamic
local field correction $G(\mathbf{q},\omega)$. In addition, we find that the
so-called static approximation constitutes a promising opportunity to obtain
high-quality data for $S(\mathbf{q},\omega)$ over substantial parts of the warm
dense matter regime.
