Song Hao, Schönmeier-Kromer Janik, Liu Ke, Viyuela Oscar, Pollet Lode, Martin-Delgado M A
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
Phys Rev Lett. 2022 Dec 2;129(23):230502. doi: 10.1103/PhysRevLett.129.230502.
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.
分数子模型提供了新型有隙量子物相的示例，这些物相包含本质上不可移动的激发，因此超出了拓扑序的传统概念。在这里，我们基于分数子模型计算量子纠错码的最优错误阈值。通过将比特翻转和相位翻转噪声的纠错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，我们得到了展现非传统子系统对称性而非更常见全局对称性的模型。我们进行大规模并行回火蒙特卡罗模拟以获得无序 - 温度相图，然后用其预测相应分数子码的最优错误阈值。值得注意的是，我们发现X - 立方分数子码显示出的最小错误阈值（7.5%）远高于三维拓扑码，如环面码（3.3%）或颜色码（1.9%）。这一结果，连同在西森莫里线上预测不存在玻璃序，表明分数子相作为量子存储平台具有巨大潜力。
