  The magnetization process of a frustrated spin-1/2 spin-dimer model on a
square lattice is investigated by means of a sign-problem-free quantum Monte
Carlo algorithm developed recently. Rich field-induced quantum phases are
discovered. We find two spin superfluids satisfying different symmetries upon
layer permutation. There exist as well two solid phases with distinct
checkerboard patterns. Besides, two kinds of spin supersolids are observed over
a finite regime of magnetic fields. The latter two phases can be stabilized
when small but nonzero spin anisotropy is present. Various field-induced
transitions among these phases are explored. Our findings may provide guidance
to the search of these interesting quantum phases in real frustrated spin-dimer
compounds.
