  We demonstrate how the quantum paraelectric ground state of SrTiO$_3$ can be
accessed via a microscopic $ab~initio$ approach based on density functional
theory. At low temperature the quantum fluctuations are strong enough to
stabilize the paraelectric phase even though a classical description would
predict a ferroelectric phase. We find that accounting for quantum fluctuations
of the lattice and for the strong coupling between the ferroelectric soft mode
and lattice elongation is necessary to achieve quantitative agreement with
experimental frequency of the ferroelectric soft mode. The temperature
dependent properties in SrTiO$_3$ are also well captured by the present
microscopic framework.
