  Current quantum devices suffer imperfections as a result of fabrication, as
well as noise and dissipation as a result of coupling to their immediate
environments. Because of this, it is often difficult to obtain accurate models
of their dynamics from first principles. An alternative is to extract such
models from time-series measurements of their behavior. Here, we formulate this
system-identification problem as a polynomial optimization problem. Recent
advances in optimization have provided globally convergent solvers for this
class of problems, which using our formulation prove estimates of the Kraus map
or the Lindblad equation. We include an overview of the state-of-the-art
algorithms, bounds, and convergence rates, and illustrate the use of this
approach to modeling open quantum systems.
