Carbonate liquids are an important class of molten salts, not just for industrial applications, but also in geological processes. Carbonates are generally expected to be simple liquids, in terms of ionic interactions between the molecular carbonate anions and metal cations, and therefore relatively structureless compared to more "polymerized" silicate melts. But there is increasing evidence from phase relations, metal solubility, glass spectroscopy and simulations to suggest the emergence of carbonate "networks" at length scales longer than the component molecular anions. The stability of these emergent structures are known to be sensitive to temperature, but are also predicted to be favoured by pressure. This is important as a recent study suggests that subducted surface carbonate may melt near the Earth's transition zone (similar to 44 km), representing a barrier to the deep carbon cycle depending on the buoyancy and viscosity of these liquids. In this study we demonstrate a major advance in our understanding of carbonate liquids by combining simulations and high pressure measurements on a carbonate glass, (K2CO3-MgCO3) to pressures in excess of 40 GPa, far higher than any previous in situ study. We show the clear formation of extended low-dimensional carbonate networks of close CO32- pairs and the emergence of a "three plus one" local coordination environment, producing an unexpected increase in viscosity with pressure. Although carbonate melts may still be buoyant in the lower mantle, an increased viscosity by at least three orders of magnitude will restrict the upward mobility, possibly resulting in entrainment by the down-going slab.