  We demonstrate how to construct the Z2*Z2 global symmetry which protects the
ground state degeneracy of cluster states for open boundary conditions. Such a
degeneracy ultimately arises because the set of stabilizers do not span a
complete set of integrals of motion of the cluster state Hamiltonian for open
boundary conditions. By applying control phase transformations, our
construction makes the stabilizers into the Pauli operators spanning the qubit
Hilbert space from which the degeneracy comes.
