Effect of decoherence for gate operations on a superconducting bosonic qubit

High-quality-factor 3D cavities in superconducting circuits are ideal candidates for bosonic logical qubits as their fidelity is limited only by the low photon loss rate. However, the transmon qubits that are used to manipulate bosonic qubits result in the emergence of additional relaxation and dephasing channels. In this work, a numerical study is performed to elucidate the effect of the various loss channels on the performance of logical gates on a bosonic qubit. A gate error model is developed that encapsulates the loss mechanisms for arbitrary gate operations and predicts experimentally achievable gate errors for bosonic qubits. The insights gleaned from this study into loss mechanisms suggest more efficient optimization algorithms that could reduce gate errors on bosonic qubits.