Simultaneous model selection and parameter estimation: A superconducting qubit coupled to a bath of incoherent two-level systems

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.