  We present a Bayesian quantum characterization framework that takes into
account uncertainties from both experimental data and the dynamical modeling of
the experiment. We demonstrate that ignoring dynamical model uncertainty may
lead to predictions that are inconsistent with the uncertainty present in
quantum data. A Bayesian framework is proposed and applied to characterize a
tantalum-based transmon device at Lawrence Livermore National Laboratory. We
demonstrate how modeling uncertainty can be represented by a Gaussian process
within the Bayesian framework, and how this approach improves the predictive
capability of Lindblad's master equations applied to the Ramsey measurement
protocol.
