Fault-tolerant photon addition for the bosonic error correction

Superconducting microwave cavities can be used for quantum computing. They offer the advantage of a large Hilbert space that allows the use of more complicated qubit encodings enabling error detection and correction. The dominant error for these bosonic codes is photon loss which can be detected. We focus on the CLY code on the dual-rail qubit. To correct for a photon loss in one of the cavities, we need to be able to add a photon to the photon loss error states without changing the superposition between the logical qubit states. We achieve this by coupling the system to an auxiliary transmon and taking advantage of the cross-Kerr effect. This allows us to tune a drive tone to drive a photon addition transition from a specific cavity Fock state. With two drive tones, we can apply a photon addition independently of both of the error states returning the cavity back to the original logical qubit space without causing a shift in the superposition between the states. We can achieve fault-tolerance, by using the transmon g and f states as the ancilla logical states for the operation. This allows us to detect transmon decay and dephasing errors by measuring the transmon state in the end. This photon addition protocol will also be useful for error correction of other bosonic codes.