arXiv 2209.112072022-09-22quant-phcs.LG

通过量子信号处理实现超越海森堡极限的量子精密测量

Beyond Heisenberg Limit Quantum Metrology through Quantum Signal Processing

University of California, Berkeley（加州大学伯克利分校）；Google Quantum AI（谷歌量子人工智能）

Yulong Dong, Jonathan Gross, Murphy Yuezhen Niu

摘要：

利用计量学中的量子效应，例如纠缠和相干，允许以增强的灵敏度测量参数。然而，与时间相关的噪声会破坏这种海森堡限制的放大。为了克服实际量子精密测量中噪声引起的局限性，我们提出了一种基于量子信号处理框架的量子测量方法。我们的算法将易受时间相关误差影响的门参数$φ$ ~（单量子比特Z相位）与目标门参数$θ$ ~（|10>和|01>状态），这在很大程度上是免费的时间相关的错误。我们的方法在超导量子位实验中学习$θ$时，达到了标准差中的$10^{-4}$弧度的准确度，比现有的替代方案高出两个数量级。我们还证明了通过快速傅立叶变换和顺序相位差学习时间相关门参数的鲁棒性。我们从理论上和数值上表明，有一个有趣的过渡的最佳计量方差缩放作为电路深度$d$的函数从前渐近制度$d \ll 1/θ$海森堡极限$d \to \infty$。值得注意的是，在前渐近制度，我们的方法的估计方差对时间敏感的参数$φ$规模快于渐近海森堡极限作为深度的函数，$\text{Var}(\hatφ)\approx 1/d^4$。我们的工作是第一个在实验室量子计算机中展示实际应用的量子信号处理算法。

英文摘要：

Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a quantum-metrology method based on the quantum-signal-processing framework to overcome these realistic noise-induced limitations in practical quantum metrology. Our algorithm separates the gate parameter $φ$~(single-qubit Z phase) that is susceptible to time-dependent error from the target gate parameter $θ$~(swap-angle between |10> and |01> states) that is largely free of time-dependent error. Our method achieves an accuracy of $10^{-4}$ radians in standard deviation for learning $θ$ in superconducting-qubit experiments, outperforming existing alternative schemes by two orders of magnitude. We also demonstrate the increased robustness in learning time-dependent gate parameters through fast Fourier transformation and sequential phase difference. We show both theoretically and numerically that there is an interesting transition of the optimal metrology variance scaling as a function of circuit depth $d$ from the pre-asymptotic regime $d \ll 1/θ$ to Heisenberg limit $d \to \infty$. Remarkably, in the pre-asymptotic regime our method's estimation variance on time-sensitive parameter $φ$ scales faster than the asymptotic Heisenberg limit as a function of depth, $\text{Var}(\hatφ)\approx 1/d^4$. Our work is the first quantum-signal-processing algorithm that demonstrates practical application in laboratory quantum computers.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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