  We present a quasiparticle self-consistent $GW$ (QSGW) implementation for
periodic systems based on crystalline Gaussian basis sets. Our QSGW approach is
based on a full-frequency analytic continuation GW scheme with Brillouin zone
sampling and employs the Gaussian density fitting technique. We benchmark our
QSGW implementation on a set of weakly-correlated semiconductors and insulators
as well as strongly correlated transition metal oxides including MnO, FeO, CoO,
and NiO. Band gap, band structure, and density of states are evaluated using
finite size corrected QSGW. We find that although QSGW systematically
overestimates band gaps of tested semiconductors and transition metal oxides,
it completely removes the dependence on the choice of density functionals and
provides more consistent prediction of spectral properties than $G_0W_0$ across
a wide range of solids. This work paves the way for utilizing QSGW in ab initio
quantum embedding for solids.
