  We determine the low-energy spectrum and Parisi replica symmetry breaking
function for the spin glass phase of the quantum Ising model with
infinite-range random exchange interactions and transverse and longitudinal
($h$) fields. We show that, for all $h$, the spin glass state has full replica
symmetry breaking, and the local spin spectrum is gapless with a spectral
density which vanishes linearly with frequency. These results are obtained
using an action functional$\unicode{x2014}$argued to yield exact results at low
frequencies$\unicode{x2014}$that expands in powers of a spin glass order
parameter, which is is bilocal in time, and a matrix in replica space. We also
present the exact solution of the infinite-range spherical quantum $p$-rotor
model at nonzero $h$: here, the spin glass state has one-step replica symmetry
breaking, and gaplessness only appears after imposition of an additional
marginal stability condition. Possible connections to experiments on random
arrays of trapped Rydberg atoms are noted.
