Quantum Information Processing

, Volume 11, Issue 6, pp 1961–1968 | Cite as

Topological order in 1D Cluster state protected by symmetry

  • W. Son
  • L. Amico
  • V. Vedral
Letter to the Editor


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.


Cluster state Topological order in many-body quantum systems 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of PhysicsSogang UniversitySeoulKorea
  2. 2.CNR-MATIS-IMM & Dipartimento di Fisica e Astronomia Universitá di CataniaCataniaItaly
  3. 3.Center for Quantum TechnologyNational University of SingaporeSingaporeSingapore
  4. 4.Department of PhysicsNational University of SingaporeSingaporeSingapore

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