Proposal for erasure conversion in integer fluxonium qubits

We propose an erasure conversion scheme on the |erangle-|frangle and |grangle-|frangle qubits in integer fluxonium qubits (IFQs), which are both first-order insensitive to 1/f flux noise. The |erangle-|frangle transition is identical to that of a usual fluxonium qubit and hence is expected to have excellent coherence time, while the |grangle-|frangle transition is additionally protected from the energy relaxation by the parity symmetry. The dominant error in both qubits arises due to the energy relaxation: from |erangle to |grangle in the e--f qubit and from |frangle to |erangle in the g--f qubit. Such errors can be treated as erasure events, and their efficient detection improves the performance of quantum error-correcting codes. We consider a protocol for such erasure conversion based on the dispersive readout. Our main finding is that, with proper circuit parameter choice, carefully designed gate sets, and the integration of erasure conversion, IFQs promise high effective coherence times.