  We prove that the empirical density of states of quantum spin glasses on
arbitrary graphs converges to a normal distribution as long as the maximal
degree is negligible compared with the total number of edges. This extends the
recent results of [6] that were proved for graphs with bounded chromatic number
and with symmetric coupling distribution. Furthermore, we generalise the result
to arbitrary hypergraphs. We test the optimality of our condition on the
maximal degree for $p$-uniform hypergraphs that correspond to $p$-spin glass
Hamiltonians acting on $n$ distinguishable spin-$1/2$ particles. At the
critical threshold $p=n^{1/2}$ we find a sharp classical-quantum phase
transition between the normal distribution and the Wigner semicircle law. The
former is characteristic to classical systems with commuting variables, while
the latter is a signature of noncommutative random matrix theory.
