  A quantum particle cannot in general diffuse through a disordered medium
because of its wavelike nature, but interacting particles can escape
localization by collectively percolating through the system. For bosonic
particles this phenomenon corresponds to a quantum transition from a localized
insulator phase - the Bose glass - to a superfluid phase, in which particles
condense into an extended state. Here, we construct a universal phase diagram
of disordered bosons in doped quantum magnets for which bosonic quasi-particles
are represented by magnetized states (spin triplets) of the quantum spins,
condensing into a magnetically ordered state. The appearance of a Bose glass
leads to strong measurable signatures in the onset of superfluidity of the
spin-triplet gas, exhibiting a complex crossover from low-temperature quantum
percolation to a conventional condensation transition at intermediate
temperatures.
