It is shown that quantum effects lead to a significant decrease of the glass transition temperature T(g) with respect to the melting temperature T(m), so that the ratio T(g)/T(m) can be much smaller than the typical value of 2/3 in materials where T(g) is near or below ~60 K. Furthermore, it is demonstrated that the viscosity or structural relaxation time in such low temperature glass formers should exhibit highly unusual temperature dependence, namely a decrease of the apparent activation energy upon approaching T(g) (instead of traditional increase).