Performance of rotation-symmetric bosonic codes in the presence of non-Markovian effects induced by random telegraph noise

Decoherence in quantum devices, such as qubits and resonators, is often caused by bistable fluctuators modeled as random telegraph noise (RTN), leading to significant dephasing. We analyze the impact of individual and multiple fluctuators on a bosonic mode in continuous variable systems, identifying non-Markovian behavior governed by two timescales: the switching rate (ξ) and the coupling strength (ν) of the fluctuator. Using the Breuer-Laine-Piilo trace-distance measure, we characterize non-Markovianity for both Gaussian and non-Gaussian states, revealing that for rotation-symmetric bosonic (RSB) codes, known for their error-correction advantages, the measure grows linearly with code symmetry and can become unbounded. We evaluate the performance of these RSB codes under simultaneous loss and RTN dephasing. For a teleportation-based Knill error-correction circuit, the codes perform robustly in the Markovian limit. In the non-Markovian regime, the performance depends nontrivially on the time at which the error correction is performed. The average gate fidelity of the error-corrected state in this case exhibits oscillations as a function of time due to the oscillatory nature of the dephasing function of the RTN noise; however, for most of the parameter ranges, the values stay beyond the breakeven point. Extending to multiple fluctuators that produce 1/f noise, we observe that non-Markovianity decays with increasing fluctuator count, while the performance of RSB codes remains effective with increasing number of fluctuators.