We discuss quantum variational optimization of Ramsey interferometry with ensembles of $N$ entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation. We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits. These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions. Optimization is defined relative to a cost function, which in the present study is the Bayesian mean squared error of the estimated phase for a given prior distribution; i.e., we optimize for a finite dynamic range of the interferometer. In analogous variational optimizations of optical atomic clocks, we use the Allan deviation for a given Ramsey interrogation time as the relevant cost function for the long-term instability. Remarkably, even low-depth quantum circuits yield excellent results that closely approach the fundamental quantum limits for optimal Ramsey interferometry and atomic clocks. The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions. While in the present work variationally optimized circuits are found with classical simulations, optimization can also be performed “on” the (physical) quantum sensor, also in regimes not accessible to classical computations and in the presence of imperfections.

中文翻译：

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拉姆齐干涉测量和原子钟的量子变分优化

我们讨论了 Ramsey 干涉测量的量子变分优化与 $N$纠缠原子，及其在基于贝叶斯相位估计方法的原子钟中的应用。我们在相应的纠缠和解码量子电路的变分近似内确定最佳输入状态和广义测量。这些电路是根据可用于特定传感器平台的基本量子操作构建的，例如单轴扭曲或有限范围交互。优化是相对于成本函数定义的，在本研究中，成本函数是给定先验分布的估计相位的贝叶斯均方误差；即，我们针对干涉仪的有限动态范围进行优化。在光学原子钟的类似变分优化中，我们使用给定 Ramsey 询问时间的艾伦偏差作为长期不稳定性的相关成本函数。值得注意的是，即使是低深度的量子电路也能产生出色的结果，非常接近最佳拉姆齐干涉测量和原子钟的基本量子极限。这里确定的量子计量方案很容易适用于基于光晶格、镊子阵列或俘获离子的原子钟。虽然在目前的工作中通过经典模拟发现了可变优化电路，但也可以在（物理）量子传感器“上”执行优化，也在经典计算无法访问的情况下和存在缺陷的情况下执行优化。这里确定的量子计量方案很容易适用于基于光晶格、镊子阵列或俘获离子的原子钟。虽然在目前的工作中通过经典模拟发现了可变优化电路，但也可以在（物理）量子传感器“上”执行优化，也在经典计算无法访问的情况下和存在缺陷的情况下执行优化。这里确定的量子计量方案很容易适用于基于光晶格、镊子阵列或俘获离子的原子钟。虽然在目前的工作中通过经典模拟发现了可变优化电路，但也可以在（物理）量子传感器“上”执行优化，也在经典计算无法访问的情况下和存在缺陷的情况下执行优化。