Adaptive Hamiltonian Estimation Using Bayesian Experimental Design

TL;DR

This paper introduces an adaptive Bayesian experimental design protocol that significantly improves the accuracy of Hamiltonian parameter estimation in quantum systems compared to traditional offline methods.

Contribution

The paper presents a novel adaptive protocol for Hamiltonian estimation that optimizes experiments based on prior data, achieving exponential accuracy improvements.

Findings

Exponential improvement in parameter estimation accuracy.

Sampling at the Nyquist rate is suboptimal.

Risk of the adaptive algorithm is near the global optimum.

Abstract

Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially improved accuracy over offline estimation strategies. To achieve this, we derive an adaptive protocol which finds the optimal experiments based on previous observations. We show that the risk associated with this algorithm is close to the global optimum, given a uniform prior. Additionally, we show that sampling at the Nyquist rate is not optimal.