  The melting curve of pure silica (SiO$_2$) was determined using {\it ab
initio} density functional theory together with the solid-liquid coexisting
approach, thermodynamic integration and the Z method. The melting curves are
consistent with a smooth slow increase in a large region from 50 GPa (dT/dP
$\approx$ 15 K/GPa) to about 500 GPa (dT/dP $\approx$ 5 K/GPa) without any
abrupt changes at around 120 GPa and 300 GPa as seen in some recent
experimental and computational studies. The topography of the melting curve
above 50 GPa is consistent with a gradual change in the distribution of the Si
coordination numbers in the liquid state and the absence of large changes in
the density following solid-solid phase transitions. The pair distribution
functions show that the structural correlation in the liquid is mainly
short-ranged and that the Si-O bond is stiff. The densification of the melt
structure with pressure above 50 GPa is therefore due to an increase in 7- and
8-fold coordinated silicon.
