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Topological order in 1D Cluster state protected by symmetry

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Abstract

We demonstrate how to construct the Z 2 × 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.

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Authors and Affiliations

  1. Department of Physics, Sogang University, Mapo-gu, Shinsu-dong, Seoul, 121-742, Korea

    W. Son

  2. CNR-MATIS-IMM & Dipartimento di Fisica e Astronomia Universitá di Catania, C/O ed. 10, viale A. Doria 6, 95125, Catania, Italy

    L. Amico

  3. Center for Quantum Technology, National University of Singapore, Singapore, 117542, Singapore

    V. Vedral

  4. Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore, 117542, Singapore

    V. Vedral

Authors
  1. W. Son
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  2. L. Amico
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  3. V. Vedral
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Corresponding author

Correspondence to L. Amico.

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Son, W., Amico, L. & Vedral, V. Topological order in 1D Cluster state protected by symmetry. Quantum Inf Process 11, 1961–1968 (2012). https://doi.org/10.1007/s11128-011-0346-7

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  • DOI: https://doi.org/10.1007/s11128-011-0346-7

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