  Bosonic quantum error-correcting codes offer a viable direction towards
reducing the hardware overhead required for fault-tolerant quantum information
processing. A broad class of bosonic codes, namely rotation-symmetric codes,
can be characterized by their phase-space rotation symmetry. However, their
performance has been examined to date only within an idealistic noise model.
Here, we further analyze the error-correction capabilities of
rotation-symmetric codes using a teleportation-based error-correction circuit.
To this end, we numerically compute the average gate fidelity, including
measurement errors into the noise model of the data qubit. Focusing on physical
measurement models, we assess the performance of heterodyne and adaptive
homodyne detection in comparison to the previously studied canonical phase
measurement. This setting allows us to shed light on the role of different
currently available measurement schemes when decoding the encoded information.
We find that with the currently achievable measurement efficiencies in
microwave optics, bosonic rotation codes undergo a substantial decrease in
their break-even potential. In addition, we perform a detailed analysis of
Gottesman-Kitaev-Preskill (GKP) codes using a similar error-correction circuit
that allows us to analyze the effect of realistic measurement models on
different codes. In comparison to RSB codes, we find for GKP codes an even
greater reduction in performance together with a vulnerability to photon-number
dephasing. Our results show that highly efficient measurement protocols
constitute a crucial building block towards error-corrected quantum information
processing with bosonic continuous-variable systems.
