Robustness of longitudinal transmon readout to ionization

Multiphoton processes deteriorate the quantum nondemolition (QND) character of the dispersive readout in circuit QED, causing the readout to lag behind single- and two-qubit gates in both speed and fidelity. Alternative methods such as longitudinal readout have been proposed; however, it is unknown to what extent multiphoton 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 multiphoton transitions can be heavily suppressed with detuning because 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, and the description of longitudinal readout in the classical limit of the transmon to qualitatively demonstrate that longitudinal readout is robust. We show that fast, high-fidelity QND readout of transmon qubits is possible with longitudinal coupling.