Bayesian Phase Estimation via Active Learning

TL;DR

This paper introduces a non-adaptive Bayesian phase estimation algorithm that uses active learning to efficiently update the auxiliary phase, achieving adaptive-like performance with simpler calculations and broad practical applications.

Contribution

The paper proposes a novel non-adaptive Bayesian phase estimation method with an active learning update rule, reducing measurement needs while maintaining high precision and robustness.

Findings

Reduces measurement count compared to traditional methods

Maintains high precision and noise robustness

Applicable to practical quantum sensors

Abstract

Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable auxiliary phase. Here, we present a non-adaptive Bayesian phase estimation (BPE) algorithms with an ingenious update rule of the auxiliary phase designed via active learning. Unlike adaptive BPE algorithms, the auxiliary phase in our algorithm is determined by a pre-established update rule with simple statistical analysis of a small batch of data, instead of complex calculations in every update trails. As the number of measurements for a same amount of Bayesian updates is significantly reduced via active learning, our algorithm can work as efficient as adaptive ones and shares the advantages (such as wide dynamic range and perfect noise robustness) of non-adaptive ones. Our algorithm is of promising applications in various practical quantum sensors such as atomic clocks and quantum magnetometers.