  In characterization of quantum systems, adapting measurement settings based
on data while it is collected can generally outperform in efficiency
conventional measurements that are carried out independently of data. The
existing methods for choosing measurement settings adaptively assume that the
model, or the number of unknown parameters, is known. We introduce simultaneous
adaptive model selection and parameter estimation. We apply our technique for
characterization of a superconducting qubit and a bath of incoherent two-level
systems, a leading decoherence mechanism in the state-of-the-art
superconducting qubits.
