Topological order in 1D Cluster state protected by symmetry

Journal article

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. © Springer Science+Business Media, LLC 2011.

Authors: Son, W; Amico, L; Vedral, V

• Journal: Quantum Information Processing
• Volume: 11
• Issue: 6
• Pages: 1961-1968
• Publication date: 2012-12-01
• DOI: 10.1007/s11128-011-0346-7
• EISSN: 1573-1332
• ISSN: 1570-0755
• Language: English
• Keywords: Cluster state; Topological order in many-body quantum systems