Floquet theory for dispersive readout in circuit QED

In circuit QED, qubit relaxation rates can depend on the strength of the measurement tone, which hinders efforts to make readout fast and high-fidelity enough for large-scale quantum error correction. Within a Floquet theory, we study the typical circuit QED setup consisting of a superconducting qubit (transmon or fluxonium) coupled to a readout resonator. We find that qubit relaxation is determined by the interplay of drive-dressed spectra and transition rates. For a number of realistic environmental couplings, we compute drive-strength-dependent qubit relaxation rates that illustrate how resonant multi-photon processes alter the quantum non-demolition character of the measurement.