  Recent progress in characterization for gapped quantum phases has also
triggered the search of universal resource for quantum computation in symmetric
gapped phases. Prior works in one dimension suggest that it is a feature more
common than previously thought that nontrivial 1D symmetry-protected
topological (SPT) phases provide quantum computational power characterized by
the algebraic structure defining these phases. Progress in two and higher
dimensions so far has been limited to special fixed points in SPT phases. Here
we provide two families of 2D $Z_2$ symmetric wave functions such that there
exists a finite region of the parameter in the SPT phases that supports
universal quantum computation. The quantum computational power loses its
universality at the boundary between the SPT and symmetry-breaking phases.
