量子存储器解码器必须了解时间相关噪声的哪些信息？

中文摘要 AI 辅助

量子纠错解码器必须了解时间相关噪声的哪些信息，以及了解这些信息的代价是什么？我们针对具有已知系统-环境相互作用的固定稳定子存储器实验研究此问题。我们将校准表述为选择泡利恢复的保真度差异，并将缺失信息与由此产生的保真度损失联系起来。我们的主要示例使用一类CSS码（包括Shor码、Steane码和奇距离旋转表面码）中的弱相干$X$旋转。所有物理量子比特共享一个符号，该符号要么在整个运行期间固定，要么在每个时间间隔独立重新绘制。这两种模型具有相同的综合征统计量和相同的时空泡利过程（SPP），该过程通过对每个噪声间隔进行泡利扭曲获得。然而，在适当的存储时间，它们需要不同的逻辑校正。在弱噪声极限下，当模型已知时，每个模型几乎可以完美校正。在没有模型信息的情况下，即使最佳最终恢复相对于噪声感知最优值的最坏情况保真度损失也接近$1/2$，尽管可以访问完整的综合征记录。对于这对模型，在固定码和低于$1/2$的固定正目标损失下，我们证明了匹配的校准界限。通过逻辑制备和最终读出，完整的QEC周期所需的噪声间隔数随码的$X$距离的倒数旋转角度的幂次缩放。在每次提取前允许两个不间断间隔可将最优代价降低到逆平方缩放。对每个噪声间隔进行物理泡利扭曲会改变恢复性能及其信息需求。丢弃所应用的随机泡利操作的记录使得SPP足以实现最优恢复。保留此记录可以提高可达到的保真度，但达到该最优值可能需要额外的噪声信息。

英文摘要

What must a quantum error-correction decoder know about temporally correlated noise, and what does it cost to learn? We study this question for fixed stabilizer memory experiments with known system-environment interactions. We formulate calibration in terms of the fidelity differences that select a Pauli recovery and relate missing information to the resulting fidelity loss. Our main example uses weak coherent $X$ rotations in a class of CSS codes including Shor, Steane, and odd-distance rotated surface codes. All physical qubits share a sign either fixed throughout a run or independently redrawn each interval. The two models have identical syndrome statistics and the same spatiotemporal Pauli process (SPP), obtained by Pauli-twirling every noise interval. Yet at suitable storage times, they require different logical corrections. In the weak-noise limit, each model is almost perfectly correctable when known. Without model information, even the best final recovery has a worst-case fidelity loss approaching $1/2$ relative to the noise-aware optimum, despite access to the full syndrome record. For this pair of models, at fixed code and fixed positive target loss below $1/2$, we prove matching calibration bounds. With logical preparation and final readout, complete QEC cycles require a number of noise intervals scaling as the inverse rotation angle raised to the code's $X$ distance. Allowing two uninterrupted intervals before one extraction reduces the optimal cost to inverse-square scaling. Physical Pauli twirling of every noise interval changes both recovery performance and its information requirements. Discarding the record of applied random Pauli operations makes the SPP sufficient for optimal recovery. Keeping this record can improve the attainable fidelity, but reaching that optimum may require additional noise information.

发表机构

• University of Waterloo（滑铁卢大学）
• Department of Applied Mathematics, University of Waterloo（滑铁卢大学应用数学系）
• National Research Council Canada（加拿大国家研究委员会）

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