  We examine the phase diagram of the $p$-interaction spin glass model in a
transverse field. We consider a spherical version of the model and compare with
results obtained in the Ising case. The analysis of the spherical model, with
and without quantization, reveals a phase diagram very similar to that obtained
in the Ising case. In particular, using the static approximation, reentrance is
observed at low temperatures in both the quantum spherical and Ising models.
This is an artifact of the approximation and disappears when the imaginary time
dependence of the order parameter is taken into account. The resulting phase
diagram is checked by accurate numerical investigation of the phase boundaries.
