Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry,Physical Review Letters

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Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
Physical Review Letters ( IF 8.1 ) Pub Date : 2022-11-30 , DOI: 10.1103/physrevlett.129.230502
Hao Song _{1,

2,

3} , Janik Schönmeier-Kromer _{4,

5} , Ke Liu _{4,

5} , Oscar Viyuela _{6,

7} , Lode Pollet _{4,

5,

8} , M A Martin-Delgado ₃

Affiliation

Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the error-correction process for bit-flip and phase-flip noises into novel statistical models with Ising variables and random multibody couplings, we obtain models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We perform large-scale parallel tempering Monte Carlo simulations to obtain disorder-temperature phase diagrams, which are then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the X-cube fracton code displays a minimum error threshold (7.5%) that is much higher than 3D topological codes such as the toric code (3.3%), or the color code (1.9%). This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms.

中文翻译：

具有子系统对称性的分形码和随机自旋模型的最佳阈值

Fracton 模型提供了物质的新型带隙量子相的示例，这些量子相具有本质上不可移动的激发，因此超出了传统的拓扑序概念。在这里，我们计算基于分形模型的量子纠错码的最佳错误阈值。通过将比特翻转和相位翻转噪声的误差校正过程映射到具有伊辛变量和随机多体耦合的新型统计模型中，我们获得了展示非常规子系统对称性而不是更常见的全局对称性的模型。我们执行大规模并行回火蒙特卡洛模拟以获得无序温度相图，然后用于预测相应分形码的最佳误差阈值。值得注意的是，我们发现 X 立方体分形代码显示了一个最小错误阈值 (7. 5%），远高于复曲面代码（3.3%）或颜色代码（1.9%）等 3D 拓扑代码。这一结果，连同预测的 Nishimori 线处玻璃秩序的缺失，显示了分形相用作量子存储平台的巨大潜力。

更新日期：2022-11-30

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