Encoding an erasure qubit in a transmon qutrit

Erasure qubits are a promising route towards scalable fault-tolerant quantum error correction. However, current proposals often require redundant hardware and significantly more gates to implement erasure checks, partially negating their advantage. In this work, we propose and analyze an error correction architecture encoding qubits in the gf manifold of transmons and concatenating them into a surface code. In this encoding, a single-excitation loss takes the transmon to the e state, outside of the logical subspace. The circuit elements for syndrome extraction are designed such that for every error correction round, each ancilla qubit of the surface code simultaneously performs an erasure check and, if the erasure check passes, a stabilizer measurement. Compared to previous proposals, the overhead cost is kept low by using a single transmon to encode the qubit, and by using the same measurement to do an erasure check and stabilizer measurement. We study the performance of the surface code using this compact erasure qubit architecture and determine the system parameters required for hardware efficiency.