论文标题
超越海森堡通过量子信号处理限制量子计量学
Beyond Heisenberg Limit Quantum Metrology through Quantum Signal Processing
论文作者
论文摘要
在纠缠和连贯性等计量学中利用量子效应使人们可以测量具有增强灵敏度的参数。但是，时间依赖性噪声会破坏这种海森堡限制的扩增。我们提出了一种基于量子信号处理框架的量子计量方法，以克服这些现实的噪声引起的实际量子计量学限制。我们的算法将门参数$φ$〜（单量Z相）分开，该算法与目标门参数$θ$〜（| 10>> 10>和| 01>状态之间的swap-angle）易受时间相关的误差，这在很大程度上无时间依赖于时间依赖性误差。我们的方法达到了$ 10^{ - 4} $径向在标准偏差的$ 10^{ - 4}的精度，用于学习超导量实验的$θ$，从而超过了两个数量级的现有替代方案。我们还通过快速的傅立叶变换和顺序相位差来证明学习时间依赖性门参数的鲁棒性增加。我们从理论上和数字上都显示出最佳计量方差缩放的有趣过渡，这是电路深度$ d $的函数，从预抗膜片前制度$ d \ ll 1/θ$到Heisenberg限制$ d \ d \ d \ d \ to \ infty $。值得注意的是，在临时制度中，我们方法对时间敏感参数的估计差异$φ$比渐近Heisenberg限制的速度快于深度，$ \ text {var}（\hatφ）（\hatφ）\ 1/d^4 $。我们的工作是第一个证明在实验室量子计算机中实用应用的量子信号处理算法。
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.
