Erasure conversion in integer fluxonium qubits

Integer fluxonium is a promising high-coherence single-mode qubit. In integer fluxonium the ground (g) and second excited (f) states make up another long-lived but inherently leaky qubit where the dominant error, which is amplitude damping from f to the first excited (e) state, can be converted to erasure by detecting population in e via dispersive readout . At the same time the qubit state in g-f subspace is weakly affected when the dispersive shifts from g and f states are matched. Because the g-f transition is forbidden by parity, elaborate gate designs are needed to operate this qubit which could potentially spoil the erasure-dominant error structure. We propose a method to make gates on g-f integer fluxonium erasure-dominant. In Raman X gate for example, large detuning suppresses intermediate state decay that causes undetectable amplitude damping, while additional leakage detection on higher fluxonium levels converts stray population from off-resonant excitation to erasure. We also discuss how 2-qubit gates on g-f integer fluxonium traversing via intermediate states can also maintain an error structure dominated by erasure.