论文标题
来自Majorana Delocalization表面代码的连贯误差阈值
Coherent error threshold for surface codes from Majorana delocalization
论文作者
论文摘要
统计力学映射提供了量子误差校正的关键见解。但是，现有的映射假定噪声不一致，因此忽略了由于伪造门旋转而引起的相干错误。我们用连贯的错误将表面代码映射为$ x $ - 或$ z $ - 旋转（替换位或相位翻转），将其映射到具有复杂耦合的二维（2D）ISING模型，然后再使用2D Majorana散射网络。我们的映射揭示了纠正相干和不连贯错误的共同点和定性差异。对于这两个方面，正如我们通过将2D网络与1D费米子链接到$ \ Mathbb {z} _2 $ -Nontrivial 2D绝缘子来明确显示的那样，错误纠正的相位图。但是，除了旋转角度$ ϕ_ \ text {th} $之外，而不是$ \ mathbb {z} _2 $ - 无线绝缘子，对于不相互分的错误，连贯的错误映射到Majoraana金属。此$ ϕ_ \ text {th} $是理论上可实现的存储阈值。我们从数字上找到$ ϕ_ \ text {th} \oft0.14π$。相应的位 - 流率$ \ sin^2（ϕ_ \ text {th}）\大约0.18 $超过已知的不一致的阈值$ p_ p_ \ text {th} \ oft0.11 $。
Statistical mechanics mappings provide key insights on quantum error correction. However, existing mappings assume incoherent noise, thus ignoring coherent errors due to, e.g., spurious gate rotations. We map the surface code with coherent errors, taken as $X$- or $Z$-rotations (replacing bit or phase flips), to a two-dimensional (2D) Ising model with complex couplings, and further to a 2D Majorana scattering network. Our mappings reveal both commonalities and qualitative differences in correcting coherent and incoherent errors. For both, the error-correcting phase maps, as we explicitly show by linking 2D networks to 1D fermions, to a $\mathbb{Z}_2$-nontrivial 2D insulator. However, beyond a rotation angle $ϕ_\text{th}$, instead of a $\mathbb{Z}_2$-trivial insulator as for incoherent errors, coherent errors map to a Majorana metal. This $ϕ_\text{th}$ is the theoretically achievable storage threshold. We numerically find $ϕ_\text{th}\approx0.14π$. The corresponding bit-flip rate $\sin^2(ϕ_\text{th})\approx 0.18$ exceeds the known incoherent threshold $p_\text{th}\approx0.11$.
