Role of relaxation in the quantum measurement of a superconducting qubit   using a nonlinear oscillator
  We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum non-demolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model to characterize the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator. 
T. Picot, A. Lupascu, S. Saito, C.J.P.M. Harmans, and J.E. Mooij