发表机构
Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对量子纠错中泄漏引起的相关错误问题，提出两种零开销的蜂窝Floquet码行走电路，通过周期性泄漏移除保持码距离，并在熵效应主导的水fall机制下优于行走表面码。
AI 中文摘要
泄漏，即量子比特不可检测地退出计算子空间的现象，通过在空间和时间上诱发相关错误，对量子纠错构成重大挑战。这些相关性降低了码阈值和有效码距离。为解决此问题，我们为蜂窝Floquet码（hFC）引入了两种零开销行走电路，称为涡旋电路和滑动电路，它们通过反交换双体测量的调度周期性地移除泄漏，同时动态保护逻辑量子比特。与之前针对hFC的动态电路不同，我们的电路保持了到Pauli错误的距离。我们进一步研究了它们在泄漏下的性能，发现对于两种泄漏噪声模型，它们可以纠正与Pauli错误一样多的泄漏错误，优于更广为人知的行走表面码。通过数值模拟，我们观察到泄漏下的有限错误率性能受到熵效应的强烈影响，产生了一个显著的水fall机制，其中逻辑错误率随物理错误率的下降速度远快于预期的距离限制缩放。在该机制中，即使渐近预测相反，hFC在错误率和亚阈值逻辑错误缩放方面也能优于同距离的行走表面码。
英文摘要
Leakage, occurring when a qubit undetectably exits the computational subspace, poses a significant challenge for quantum error correction by inducing correlated errors in space and time. These correlations reduce both the code threshold and the effective code distance. To address this challenge, we introduce two zero-overhead walking circuits for the honeycomb Floquet code (hFC), termed the swirling and sliding circuits, which periodically remove leakage while dynamically protecting logical qubits via a schedule of anticommuting two-body measurements. Unlike previous dynamic circuits for the hFC, ours preserves the distance to Pauli errors. We further study their performance under leakage and find that, for two leakage noise models, they may correct as many leakage errors as Pauli errors, improving on the more widely known walking surface code. Through numerical simulation, we observe that finite-error-rate performance under leakage is strongly influenced by entropic effects, producing a pronounced waterfall regime in which the logical error rate decreases much more rapidly with physical error rate than the expected distance-limited scaling. In this regime, even when asymptotic predictions suggest otherwise, the hFC can outperform the same-distance walking surface code in error rates and sub-threshold logical error scaling.
Comments10 pages main text (11 figures), 7 pages appendix
