Scalable Bayesian learning of local Hamiltonians and Lindbladian

As the size of quantum devices continues to grow, the development of scalable methods to characterise and diagnose noisy devices is becoming an increasingly important problem. Recent results demonstrate how a local Hamiltonians and Lindbladians can be reconstructed from a single, arbitrary steady state with a number of measurements that scales efficiently in the size of the system. These methods, however, can only characterise the system up to scalar factor and lack sufficient robustness to noise, both of which are imperative to be of practical use. In this talk I will present a Bayesian method that addresses both of these issues by making use of any, or all, of the following: experimental control of Hamiltonian couplings, the preparation of multiple states and the availability of any prior information we may already have for the Hamiltonian couplings. Moreover we provide an adaptive measurement protocol that can be performed online, updating estimates and their corresponding uncertainties as experimental data becomes available.