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

机译:拓扑阶段的鲁棒性:平行磁场中的拓扑颜色代码

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The robustness of the topological color code, which is a class of error-correcting quantum codes, is investigated under the influence of a 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.
机译:在均匀磁场对蜂窝晶格的影响下,研究了一类纠错量子码拓扑颜色码的鲁棒性。我们的研究依靠在低场和高场的极限中使用扰动连续unit变换,精确对角化和经典近似的两个高阶级数展开。我们表明,在单个平行场中的拓扑颜色代码与三角形格上横向场中的Baxter-Wu模型是等光谱的。发现拓扑相在临界场之前是稳定的,超过临界场后,它会通过一阶相变分解为极化相。结果还表明,在并行磁场中,拓扑颜色代码比复曲面代码更健壮。

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