通过故障计数高效估计逻辑灵敏度
Efficient Estimation of Logical Sensitivities Through Fault-Counting
- Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于故障计数的可微估计器，从单次蒙特卡洛数据中同时获取所有逻辑灵敏度，在表面码模拟中减少一至两个数量级的采样次数，并用于错误预算、单比特灵敏度和阈值追踪。
AI中文摘要：
量子纠错电路受到多种物理噪声机制的影响，必须理解这些机制对逻辑故障的贡献，以评估代码性能并指导硬件改进。对于错误类型 $i$，其个体错误预算贡献可通过逻辑灵敏度 $\nu_i = \frac{\partial p_L}{\partial p_i}$ 来表征，该量衡量逻辑错误率 $p_L$ 对每个物理噪声参数 $p_i$ 的响应。通常，$\nu_i$ 使用线性拟合（如有限差分法）测量，即在两个或多个 $p_i$ 值处测量 $p_L$ 以计算偏导数。在本文中，我们开发了一种可微估计器，利用底层故障配置的信息，从单个噪声配置下的单一蒙特卡洛数据集中同时获得 $\nabla_{\mathbf p}p_L$ 的所有分量。在具有电路级噪声的表面码模拟中，该估计器与常规有限差分法结果一致，同时实现相同方差所需的采样次数减少一至两个数量级。我们应用该技术来量化错误预算、解析单个量子比特级别的灵敏度，并推断有效码距。最后，我们将灵敏度纳入牛顿求根法，以在多维噪声模型中定位和追踪阈值轮廓。这些结果为从标准量子纠错模拟中提取和应用逻辑灵敏度信息提供了一种高效方法。
英文摘要：
Quantum error-correcting circuits are affected by multiple physical noise mechanisms, whose contributions to logical failure must be understood to evaluate code performance and guide improvements in hardware. The individual error budget contributions for an error type $i$ can be characterized by its logical sensitivity $ν_i = \frac{\partial p_L}{\partial p_i}$, which measures the response of the logical error rate $p_L$ to each physical noise parameter $p_i$. Normally, $ν_i$ is measured using linear fits such as finite differences, where $p_L$ is measured at two or more values of $p_i$ to calculate partial derivatives. In this paper, we develop a differentiable estimator to obtain all components of $\nabla_{\mathbf p}p_L$ simultaneously from a single Monte Carlo data set at one noise configuration, using information about the underlying fault configurations. In surface code simulations with circuit-level noise, the estimator agrees with conventional finite differences while requiring one to two orders of magnitude fewer shots to achieve the same variance. We apply this technique to quantify error budgets, resolve sensitivities at the individual qubit level, and infer effective code distance. Finally, we incorporate the sensitivities into Newton root finding to locate and trace threshold contours in multidimensional noise models. These results provide an efficient method for extracting and applying logical sensitivity information from standard quantum error correction simulations.
