Saeed S. Jahromi, Mehdi Kargarian, S Farhad Masoudi, Kai Phillip Schmidt
The robustness of the topological color code, which is a class of error correcting quantum codes, is investigated under the influence of an uniform magnetic field on the honeycomb lattice. Our study relies on two high-order series expansions using perturbative continuous unitary transformations in the limit of low and high fields as well as a classical approximation. We show that the topological color code in a single parallel field is isospectral to the Baxter-Wu model in a transverse field on the triangular lattice. It is found that the topological phase breaks down to the polarized phase by a first-order phase transition indicating that the topological color code is rather robust under external perturbations. The results also suggest that the topological color code is more robust than the toric code, in the parallel magnetic field.
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http://arxiv.org/abs/1211.1687
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