Robustness of longitudinal transmon readout to ionization

Multi-photon processes deteriorate the quantum non-demolition (QND) character of the dispersive readout in circuit QED, causing readout to lag behind single and two-qubit gates, in both speed and fidelity. Alternative methods such as the longitudinal readout have been proposed, however, it is unknown to what extent multi-photon processes hinder this approach. Here we investigate the QND character of the longitudinal readout of the transmon qubit. We show that the deleterious effects that arise due to multi-photon transitions can be heavily suppressed with detuning, owing to the fact that the longitudinal interaction strength is independent of the transmon-resonator detuning. We consider the effect of circuit disorder, the selection rules that act on the transmon, as well as the description of longitudinal readout in the classical limit of the transmon to show qualitatively that longitudinal readout is robust. We show that fast, high-fidelity QND readout of transmon qubits is possible with longitudinal coupling.