On the robustness of topological quantum codes: Ising perturbation

Abstract

We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse field. Such a mapping is derived by re-writing the initial Hamiltonian in a new basis so that the final model in such a basis has a well-known approximated phase transition point. Specifically, we consider the toric codes and the color codes on some various lattices with Ising perturbation. Our results provide a useful table to compare the robustness of the topological codes and to explicitly show that the robustness of the topological codes depends on triangulation of their underlying lattices.

15 pages, 12 figures, 1 table, Accepted for publication in Physical Review A

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Cited by in corpus (5)

• A strong-weak coupling duality between two perturbed quantum many-body systems: CSS codes and Ising-like systems
• Phase transition in a noisy Kitaev toric code model
• General scheme for preparation of different topological states on the cluster states
• Noisy Toric code and random bond Ising model: The error threshold in a dual picture
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase