Predicting bit-flip rates in dissipatively stabilized cat qubits

Bosonic cat qubits exhibit a favorable noise bias, exponentially suppressing bit-flip errors at the cost of a linear increase in phase-flip errors. This exponential suppression is inherited from the decreasing rate of tunneling between the two stable distant coherent states that define the cat code. Numerical and experimental evidence have shown that traditional perturbative approaches fail to accurately predict the bit-flip rate. Capturing the inherently non-perturbative processes at play remains a significant challenge.

In this work, we use Keldysh path integral techniques to predict the scaling of the bit-flip rate under various perturbations. By exploiting a hidden symmetry of the system, we derive analytical expressions for the bit-flip rate and validate these results through numerical diagonalization. Our non-perturbative approach provides a more accurate framework for understanding and estimating the error dynamics of cat qubits in the large cat-state regime. These results offer practical insights for minimizing errors in future designs, and open new avenues for investigating other non-perturbative processes.