  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.
