Selective darkening gate for g-f integer fluxonium erasure detection

|g> and |f> states form a highly coherent qubit computational subspace in integer fluxonium, but this configuration requires erasure detection of state |e>. A two-outcome dispersive-readout on the qutrit subspace requires precisely tuning the frequency of a resonator, and nontheless still suffers from dephasing in the computational subspace. We propose to do a CNOT-like gate on the fluxonium to conditionally excite a transmon ancilla, which can then be readout to detect erasure |e> state. We analyze three methods of achieving the conditional population transfer, we incorporate optimal control, and analyze their error decompositions. We conclude that selective darkening is an efficient and effective scheme to achieve the erasure detection. Since high-fidelity fluxonium selective darkening gates and fast transmon measurements have been demonstrated in experiments, our proposal further enhances the practicality of g-f integer fluxonium.