Topological order in 1D Cluster state protected by symmetry

Details Topological order in 1D Cluster state protected by symmetry Topological order in 1D Cluster state protected by symmetry

2011-11-30

arxiv.org/abs/1111.7173v2

Physics

Quantum Physics

1 figure, To be published in Quantum Information Processing

Scientific paper

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.

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