We study measurement-based quantum computation (MQC) using as quantum resource the planar code state on a two-dimensional square lattice (planar analogue of the toric code). It is shown that MQC with the planar code state can be efficiently simulated on a classical computer if at each step of MQC the sets of measured and unmeasured qubits correspond to connected subsets of the lattice.
@article{arxiv.quant-ph/0610162,
title = {On measurement-based quantum computation with the toric code states},
author = {Sergey Bravyi and Robert Raussendorf},
journal= {arXiv preprint arXiv:quant-ph/0610162},
year = {2009}
}