Modeling coherent-state lifetime in Kerr-cat qubits - Part 3/3

The Kerr-cat qubit is encoded in even and odd superpositions of coherent states and is realized by applying a squeezing drive to a Kerr nonlinear oscillator. The possibility to extend the coherent-state lifetime by increasing the squeezing amplitude makes the Kerr-cat qubit an attractive realization of a biased-noise qubit. Experiment shows that this lifetime indeed increases as a function of squeezing amplitude, but only does so abruptly whenever a new pair of the Kerr-cat's energy levels become quasi-degenerate. How can theory explain the surprising connection between the energy levels and the coherent-state lifetime? Assuming single-photon loss and gain, we observe that one eigenvalue of the Lindbladian super-operator largely determines the coherent-state lifetime. By calculating this eigenvalue perturbatively, we show that the lifetime is limited by leakage into levels outside the Kerr-cat qubit's double-well potential. Whenever a pair of levels fall into the double well and become quasi-degenerate, leakage out of the double well is reduced, leading to an abrupt increase in the coherent-state lifetime. Our Lindbladian approach complements direct master equation simulations and additionally identifies the important eigenstates of the system.