  Motivated by the noisy and fluctuating behavior of current quantum computing
devices, this paper presents a data-driven characterization approach for
estimating transition frequencies and decay times in a Lindbladian dynamical
model of a superconducting quantum device. The data includes parity events in
the transition frequency between the first and second excited states. A simple
but effective mathematical model, based upon averaging solutions of two
Lindbladian models, is demonstrated to accurately capture the experimental
observations. A deterministic point estimate of the device parameters is first
performed to minimize the misfit between data and Lindbladian simulations.
These estimates are used to make an informed choice of prior distributions for
the subsequent Bayesian inference. An additive Gaussian noise model is
developed for the likelihood function, which includes two hyper-parameters to
capture the noise structure of the data. The outcome of the Bayesian inference
are posterior probability distributions of the transition frequencies, which
for example can be utilized to design risk neutral optimal control pulses. The
applicability of our approach is demonstrated on experimental data from the
Quantum Device and Integration Testbed (QuDIT) at Lawrence Livermore National
Laboratory, using a tantalum-based superconducting transmon device.
