Readout-induced leakage of the fluxonium qubit

Dispersive readout is widely used to perform quantum nondemolition (QND) measurement on superconducting qubits. Readout fidelity can be improved by increasing the average number of photons used for readout, which should result in better SNR. Recently, it has been observed in transmons that increasing the number of readout photons leads to non-QND effects. Such non-QND effects may be worse in the fluxonium and would bottleneck the development of a fluxonium-based quantum processor. Here, we experimentally investigate the evolution of fluxonium qubits in the presence of varying numbers of readout photons. We observe that readout photons induce transitions in the fluxonium both within and outside the qubit subspace. We explore the dependence of these effects on coupling between the readout resonator and the fluxonium, and on the resonator frequency. We use the system Hamiltonian along with Floquet theory to model our experiment and find it necessary to include an external two-level-system to fully explain our observations. Finally, we present fluxonium and resonator design considerations to optimize readout parameters.