Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements*

We further analyze the error correction performance of rotation-symmetric (RSB) codes using a Knill-type error correction circuit (ECC) including measurement errors into the noise model of the data qubit. Focusing on physical measurements models, we assess the performance of heterodyne and adaptive homodyne detection in comparison to the previously studied canonical phase measurement. We find that with the current measurement efficiencies in microwave optics, RSB codes undergo a substantial decrease in their break-even potential. The results are compared to GKP codes using a similar ECC which shows a greater reduction in performance together with a vulnerability to photon dephasing. Our results show that highly efficient measurement protocols are an important part of error-corrected quantum information processing with bosonic codes.