  By means of the recently developed algorithm based on the tensor product
states, the magnetization process of frustrated spin-1/2 spin-dimer models on a
square lattice is investigated. Various field-induced quantum phases are
discovered. In particular, clear evidence of a supersolid phase over a finite
regime of magnetic field is observed. Critical fields at various field-induced
transitions are determined accurately. Our work not only implies that the
employed numerical technique can be an efficient algorithm even for the
frustrated spin systems, but also shed light on the search of the supersolid
phase in real frustrated spin-dimer compounds.
