Measurement-Induced State Transitions in a Superconducting Qubit: Part II, Theory

Dispersive readout of superconducting qubits is performed by driving a resonator that is coupled to the qubit in order to measure the state-dependent frequency shift of the resonator and infer the qubit state. Experiments have shown that when the resonator photon number exceeds a certain threshold, the qubit is excited out of its computational subspace, which we refer to as a measurement-induced state transition. These transitions degrade readout fidelity, and constitute leakage which precludes further operation of the qubit in e.g. error correction. Here we study these transitions using a transmon qubit by experimentally measuring their dependence on qubit frequency and average photon number, in the regime where the resonator frequency is lower than the qubit frequency. We observe signatures of resonant transitions between levels in the coupled qubit-resonator system that exhibit noisy behavior when measured repeatedly in time. We provide a semi-classical model of these transitions based on the rotating wave approximation and use it to predict the onset of transitions versus frequency and photon number. Our results suggest the transmon is excited to levels near the top of its cosine potential, and that offset charge dispersion can explain the observed noisy dynamics of these transitions.