Flux-pump-induced degradation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mi>T</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math> for dissipative cat qubits

Engineering nonlinear dissipation through parametric interactions is a key ingredient in autonomous quantum error correction. In ``cat'' qubits bit-flip errors may be exponentially suppressed using two-photon driven dissipation, but spurious dissipative channels appear, in a process that is poorly understood. The authors turn to high-order perturbation theory and exact numerical diagonalization to classify the possible decay mechanisms that reduce the coherence of such a qubit, bridging the gap between the microscopic parameters of the circuit and the lifetimes of the modes. Furthermore, engineering constraints on the surrounding apparatus are identified, to reduce decoherence.