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arXiv · 1211.1687

Robustness of a topological phase: Topological color code in parallel magnetic field

Saeed S. Jahromi·Mehdi Kargarian·S Farhad Masoudi·Kai Phillip Schmidt
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Abstract

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, exact diagonalization and 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 is stable up to a critical field beyond which it breaks down to the polarized phase by a first-order phase transition. 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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Saeed S. Jahromi, Mehdi Kargarian, S Farhad Masoudi, Kai Phillip Schmidt. 2013-04-01. Robustness of a topological phase: Topological color code in parallel magnetic field. https://doi.org/10.1103/physrevb.87.094413

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