Low Cost Bayesian Experimental Design for Quantum Frequency Estimation with Decoherence

TL;DR

This paper introduces WES, a low-cost adaptive Bayesian experimental design method for quantum frequency estimation, which outperforms existing heuristics and approaches the fundamental Heisenberg limit.

Contribution

The paper presents WES, a novel empirical cost-reduction strategy for quantum frequency estimation that improves efficiency and scalability over previous heuristics.

Findings

WES achieves the fastest learning rate among tested methods.

WES saturates the Heisenberg limit in simulations.

WES reduces optimization overhead significantly.

Abstract

A two-level quantum system evolving under a time-independent Hamiltonian produces oscillatory measurement probabilities. The estimation of the associated frequency is a cornerstone problem in quantum metrology, sensing, calibration and control. In this work, we tackle this task by introducing WES: a Window Expansion Strategy for low cost adaptive Bayesian experimental design. WES employs empirical cost-reduction techniques to keep the optimization overhead low, curb scaling problems, and enable high degrees of parallelism. Unlike previous heuristics, it offers adjustable classical processing costs that determine the performance standard. As a benchmark, we analyze the performance of widely adopted heuristics, comparing them with the fundamental limits of metrology and a baseline random strategy. Numerical simulations show that WES delivers the most reliable performance and fastest learning rate, saturating the Heisenberg limit.