诊断与修复魔法态培育中退化的容错距离
Diagnosing and Restoring the Degraded Fault Distance of Magic State Cultivation
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中文总结 AI 辅助
本文解析证明T态培育因泡利钩错误导致容错距离退化，并设计标志检测该错误，将逃逸前逻辑错误率从O(p^3)降至O(p^5)，在p=10^-3时实现4.9倍改进。
中文摘要 AI 辅助
T态培育是一种资源高效的协议，用于产生逻辑T态，但最近的基准测试表明，其逻辑错误率远高于预期，即高于S态培育（产生逻辑S态的类似协议）的错误率。在本文中，我们通过解析证明解释了这一T-S差异：在电路级去极化噪声下，距离-3（-5）的T态培育具有容错距离2（3），这是由于泡利钩错误在其最终双校验电路后传播为相干克利福德错误；此类错误在S态培育中保持为泡利错误，因此S态培育保留容错距离3（5）。作为分析的一部分，我们推导了一个通用公式，以及一个固定逻辑量子比特数下时间复杂度为$\mathcal O(n^3)$的算法，用于计算受克利福德错误影响的逻辑混合态的接受概率，其中$n$是物理量子比特数。然后，我们设计了标志来检测培育中的恶性钩错误，将逃逸前逻辑错误率从$\mathcal O(p^3)$改善到$\mathcal O(p^5)$。在噪声水平$p =10^{-3}$时，这实现了4.9倍的改进，但每次接受样本的尝试次数增加了1.36倍。
英文摘要
T-state cultivation is a resource-efficient protocol producing logical T states but recent benchmarks show that its logical error rate is considerably higher than intended i.e. than S-state cultivation, which is the analogous protocol for producing logical S states. In this paper, we explain this T-S discrepancy by analytically showing, under circuit-level depolarising noise, that distance-3 (-5) T-state cultivation has fault distance 2 (3) due to Pauli hook errors that propagate to coherent Clifford errors after its final double-check circuit; such errors remain Pauli in S-state cultivation, which consequently retains fault distance 3 (5). As part of our analysis we derive a general formula, and an $\mathcal O(n^3)$-time algorithm for fixed logical-qubit count, for the acceptance probability of a logical mixed state afflicted with a Clifford error, where $n$ is the physical qubit count. We then design flags that detect the malignant hook errors in cultivation, improving the pre-escape logical error rate from $Θ(p^3)$ to $Θ(p^5)$. At noise level $p =10^{-3}$, this is a 4.9$\times$ improvement, costing a 1.36$\times$ increase in attempts per accepted shot.
发表机构
- University of Oxford（牛津大学）
- The University of Osaka（大阪大学）
- Quantum Motion（量子运动）
- Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。
