The structures and the viscosities of the carbonate melts at high pressures and temperatures relevant to the Earth’s mantle condition are very important for understanding the chemical state of carbon and the deep carbon cycle. We have performed first-principles molecular dynamics calculations of the calcium carbonate (CaCO₃) melts up to 52.5 GPa. The calculations reproduce the ultralow viscosity measured by experiments and confirm the ideal liquid like behavior of calcium carbonate melts attributed to the uncorrelated diffusion of Ca²⁺ and CO₃^2- ions at pressures below 10 GPa. However, the cations and the anions  become increasingly correlated and result in significantly increased viscosities at higher pressures. Moreover, the influences of the sodium cations on the viscosities of the carbonate melts are also investigated. The addition of the sodium atoms will further lower the visocities of the carbonate melts. The present results show the transport properties of mineral melts under Earth’s lower mantle or core conditions may not be simply extrapolated from the measured results at low pressures.