Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks

TL;DR

This paper presents a variational quantum approach to optimize Ramsey interferometry and atomic clocks, achieving near-optimal precision with low-depth circuits across various quantum sensor platforms.

Contribution

It introduces a variational optimization framework for quantum interferometry and atomic clocks, identifying optimal states and measurements within practical quantum circuits.

Findings

Low-depth quantum circuits nearly reach fundamental quantum limits.

Optimization improves phase estimation accuracy over classical methods.

Applicable to diverse atomic clock platforms like optical lattices and trapped ions.

Abstract

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 square 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.