Robust online Hamiltonian learning

TLDR

The study combines sequential Monte Carlo and Bayesian experimental design to infer the dynamical parameters of a quantum system. The algorithm is designed for practical online use, balancing computational and experimental resources, and includes an online estimate of the Cramer–Rao lower bound. It successfully learns Hamiltonian parameters even when they vary between experiments and when unknown noise processes are present.

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.