  We develop a theory for the quantum vortex glass, with both the coupling
strengths and the site energies disordered. This model is closely related to XY
spin glasses and bosons in random media. For properly chosen distributions of
the site disorder the phase diagram consists of a superfluid phase, and Weak
and Strong Glass regions, dominated by long range and local fluctuations,
respectively. The most direct experimental manifestation of the Strong Glass
transition is the lack of divergence of the corresponding non-linear
susceptibility.
