Robust Online Hamiltonian Learning

TL;DR

This paper presents an online, resource-efficient algorithm that combines sequential Monte Carlo and Bayesian experimental design to accurately learn quantum Hamiltonian parameters in real-time, even amid noise and parameter changes.

Contribution

It introduces a practical, online learning algorithm that adapts to changing parameters and noise, integrating Monte Carlo methods with Bayesian design for quantum systems.

Findings

Capable of real-time Hamiltonian parameter estimation

Handles changing parameters and unknown noise

Numerically estimates the Cramer-Rao bound

Abstract

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.