发表机构
Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University; Institute for Theoretical Physics, Leibniz University Hannover（维尔纽斯大学数学与信息学院数据科学与数字技术研究所; 汉诺威莱布尼茨大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基于CSS码的量子计量学协议，证明离散时间纠错可在有限时间窗口内保持海森堡标度，并分析Steane和Shor码的纠错动力学与最优询问时间。
AI 中文摘要
量子计量学的目标是以优于经典精度估计未知参数，并理想地达到海森堡标度。然而，在实际环境中，噪声会大幅削弱这一优势，并在许多情况下使性能恢复到类似标准量子极限的水平。因此，保持量子增强需要抗噪声策略，这可以通过量子纠错来实现。在本工作中，我们开发并分析了一种基于Calderbank-Shor-Steane（CSS）码的量子计量学协议。主要结果是，对于垂直于传感哈密顿量的噪声，离散时间纠错在有限询问时间窗口内保持类似海森堡的时间标度，该窗口的持续时间取决于纠错频率。进一步表明，在传感演化后仅进行恢复操作，在所考虑的设置中对相应的未纠错噪声协议不提供计量学优势。我们为任意CSS码开发了一个分析框架，并将其应用于Steane码和Shor码，确定了离散时间纠错动力学、类似海森堡到类似SQL的交叉以及最优询问时间，并进行了数值分析。
英文摘要
The goal of quantum metrology is to estimate an unknown parameter with better-than-classical precision and, ideally, to attain Heisenberg scaling. In realistic settings, however, noise can substantially reduce this advantage and, in many cases, restore standard-quantum-limit-like performance. Preserving the quantum enhancement therefore requires noise-robust strategies, which can be implemented using quantum error correction. In this work, we develop and analyze a quantum-metrology protocol based on Calderbank-Shor-Steane (CSS) codes. The main result is that, for noise perpendicular to the sensing Hamiltonian, discrete-time error correction preserves Heisenberg-like temporal scaling over a finite interrogation-time window whose duration depends on the correction frequency. It is further shown that recovery applied only after the sensing evolution provides no metrological advantage over the corresponding uncorrected noisy protocol in the setup considered here. An analytical framework is developed for arbitrary CSS codes and applied to the Steane and Shor codes, for which the discrete-time corrected dynamics, the Heisenberg-like-to-SQL-like crossover, and the optimal interrogation time are determined and numerically analysed.
Comments24 pages, 6 figures
