Title: Optimal Low-Depth Quantum Signal-Processing Phase Estimation Show Chinese title

Title: 最优低深度量子信号处理相位估计

Abstract: Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder Heisenberg-limited amplification. We introduce Quantum Signal-Processing Phase Estimation algorithms that are robust against these challenges and achieve optimal performance as dictated by the Cram\'{e}r-Rao bound. These algorithms use quantum signal transformation to decouple interdependent phase parameters into largely orthogonal ones, ensuring that time-dependent errors in one do not compromise the accuracy of learning the other. Combining provably optimal classical estimation with near-optimal quantum circuit design, our approach achieves a standard deviation accuracy of $10^{-4}$ radians for estimating unwanted swap angles in superconducting two-qubit experiments, using low-depth ($<10$) circuits. This represents up to two orders of magnitude improvement over existing methods. Theoretically and numerically, we demonstrate the optimality of our algorithm against time-dependent phase errors, observing that the variance of the time-sensitive parameter $\varphi$ scales faster than the asymptotic Heisenberg scaling in the small-depth regime. Our results are rigorously validated against the quantum Fisher information, confirming our protocol's ability to achieve unmatched precision for two-qubit gate learning. Show Chinese abstract

Abstract: 量子效应如纠缠和相干放大可以用来显著提高量子参数估计的准确性，超越经典极限。 然而，诸如退相干和时变误差等挑战阻碍了海森堡极限的放大。 我们引入了量子信号处理相位估计算法，这些算法对这些挑战具有鲁棒性，并且按照Cramér-Rao界限实现了最佳性能。 这些算法使用量子信号变换将相互依赖的相位参数解耦为大致正交的参数，确保一个中的时变误差不会影响另一个的准确性。 结合可证明最优的经典估计和近最优的量子电路设计，我们的方法在超导双量子比特实验中估计不需要的交换角度时，实现了$10^{-4}$弧度的标准差精度，使用低深度（$<10$）电路。 这比现有方法提高了多达两个数量级。 从理论上和数值上，我们证明了算法在时变相位误差下的最优性，观察到时间敏感参数$\varphi$的方差在浅深度范围内比渐近海森堡尺度增长得更快。 我们的结果经过量子费舍尔信息的严格验证，证实了我们协议在双量子比特门学习中实现无与伦比精度的能力。