  We consider the free energy of a mean-field quantum spin glass described by a
$ p $-spin interaction and a transversal magnetic field. Recent rigorous
results for the case $ p= \infty $, i.e. the quantum random energy model
(QREM), are reviewed. We show that the free energy of the $ p $-spin model
converges in a joint thermodynamic and $ p \to \infty $ limit to the free
energy of the QREM.
