  By considering the quantum dynamics of a transverse field Ising spin glass on
the Bethe lattice we find the existence of a many body localized region at
small transverse field and low temperature. The region is located within the
thermodynamic spin glass phase. Accordingly, we conjecture that quantum
dynamics inside the glassy region is split in a small MBL and a large
delocalized (but not necessarily ergodic) region. This has implications for the
analysis of the performance of quantum adiabatic algorithms.
