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Quantum paraelectricity is a type of incipient ferroelectricity where the onset of ferroelectric order is suppressed by quantum fluctuations. From the soft mode theory of ferroelectricity, this occurs when a ferroelectric instability is stabilized by quantum fluctuations. In this case the soft-mode frequency never becomes unstable as opposed to a regular ferroelectric.
Experimentally this is associated with an anomalous behaviour of the dielectric susceptibility, for example in SrTiO3. In a normal ferroelectric, close to the onset of the phase transition the dielectric susceptibility diverges as the temperature approaches the Curie temperature. However, in the case of a quantum paraelectric the dielectric susceptibility diverges until it reaches a temperature low enough for quantum effects to cancel out the ferroelectricity. In the case of SrTiO3 this is around 4K.
Other known quantum paraelectrics are KTaO3 and potentially CaTiO3.