  We solve the $S=1/2$ infinite-range random Heisenberg Hamiltonian in the
paramagnetic phase using quantum Monte Carlo and analytical techniques. We find
that the spin-glass susceptibility diverges at a finite temperature $T_g$ which
demonstrates the existence of a low-temperature ordered phase. Quantum
fluctuations reduce the critical temperature and the effective Curie constant
with respect to their classical values. They also give rise to a redistribution
of spectral weight in the dynamic structure factor in the paramagnetic phase.
As the temperature decreases the spectrum of magnetic excitations gradually
splits into quasi-elastic and inelastic contributions whose weights scale as
$S^2$ and $S$ at low temperature.
