  The liquid regime equation of state of silicon dioxide SiO$_2$ is calculated
via quantum molecular dynamics in the density range 5 to 15 g/cc and with
temperatures from 0.5 to 100 eV, including the $\alpha$-quartz and stishovite
phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density
functional theory (DFT), above 8 eV a new orbital-free DFT formulation,
presented here, based on matching Kohn-Sham DFT calculations is employed.
Recent experimental shock data is found to be in very good agreement with the
current results. Finally both experimental and simulation data are used in
constructing a new liquid regime equation of state table for SiO$_2$.
