Robust Online Hamiltonian Learning

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. 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. We further illustrate the practicality of our algorithm by applying it to two test problems: (1) learning an unknown frequency and the decoherence time for a single-qubit quantum system and (2) learning couplings in a many-qubit Ising model Hamiltonian with no external magnetic field.