Symmetry-protected topological phases with uniform computational power   in one dimension
  We investigate the usefulness of ground states of quantum spin chains with symmetry-protected topological order (SPTO) for measurement-based quantum computation. We show that, in spatial dimension one, if an SPTO phase supports quantum wire, then, subject to an additional symmetry condition that is satisfied in all cases so far investigated, it can also be used for quantum computation. 
Robert Raussendorf, Dongsheng Wang, Abhishodh Prakash, Tzu-Chieh Wei,   David Stephen
quant-ph