Topological order in 1D Cluster state protected by symmetry

  • Authors:

  • W. Son;L. Amico;V. Vedral

  • Affiliations:

  • Department of Physics, Sogang University, Seoul, Korea 121-742;CNR-MATIS-IMM & Dipartimento di Fisica e Astronomia Universitáá di Catania, Catania, Italy 95125;Center for Quantum Technology, National University of Singapore, Singapore, Singapore 117542 and Department of Physics, National University of Singapore, Singapore, Singapore 117542

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2012

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Abstract

We demonstrate how to construct the Z 2 脳 Z 2 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.