平面拓扑码的精确模拟不能使用循环边界
Accurate simulations of planar topological codes cannot use cyclic boundaries
摘要：
循环边界在物理学和数学的许多分支中使用，通常用于辅助大空间的近似。我们表明，当确定平面，容错，拓扑量子纠错的性能，使用循环边界导致显着低估的逻辑错误率。我们提出了循环和非循环的表面码模拟表现出这种差异，并精确地再现所观察到的行为在低物理误差的限制分析公式。这些渐近公式然后被用来证明，低估是指数大的码距离d在任何固定的物理错误率p低于阈值错误率p_th。
英文摘要：
Cyclic boundaries are used in many branches of physics and mathematics, typically to assist the approximation of a large space. We show that when determining the performance of planar, fault-tolerant, topological quantum error correction, using cyclic boundaries leads to a significant underestimate of the logical error rate. We present cyclic and non-cyclic surface code simulations exhibiting this discrepancy, and analytic formulae precisely reproducing the observed behavior in the limit of low physical error. These asymptotic formulae are then used to prove that the underestimate is exponentially large in the code distance d at any fixed physical error rate p below the threshold error rate p_th.
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