Modeling fluxonium readout with Floquet dynamics and two-level systems

Fluxonium is a promising superconducting qubit, but experiments have faced unique difficulties in achieving quantum non-demolition (QND) dispersive measurement. High-fidelity QND readout, which is a necessary primitive operation for quantum computation, has been hampered in the fluxonium by an anomalous decrease in the qubit's survival probability as the readout photon population grows. While Floquet resonator-fluxonium Hamiltonian dynamics predicts some of the observed transitions, such dynamics do not capture both non-monotonic and seemingly non-unitary behavior of the transition probabilities. We present a model that predicts how two-level systems near the qubit frequency interact with the Floquet dynamics of the driven fluxonium-resonator system, and we show that we are able to accurately model experimental data using this framework.