Hamiltonian Learning with Online Bayesian Experiment Design in Practice

Estimating parameters of quantum systems is usually done by performing a sequence of predetermined experiments and post-processing the resulting data. It is known that online design, where the choice of the next experiment is based on the most up-to-date knowledge about the system, can offer speedups to parameter estimation. We apply online Bayesian experiment design to a Nitrogen Vacancy (NV) in diamond to learn the values of a five-parameter model describing its Hamiltonian and decoherence process. Comparing this to standard pre-determined experiment sweeps, we find that we can achieve median posterior variances on some parameters that are between 10 and 100 times better given the same amount of data. This has applications to NV magnetometry where one of the Hamiltonian coefficients is the parameter of interest. Furthermore, the methods that we use are generic and can be adapted to any quantum device.