How the Kerr-Cat Qubit Dies-And How to Rescue It

Abstract: Kerr-cat qubits have been experimentally shown to exhibit a large noise bias, with one decay channel suppressed by several orders of magnitude. In superconducting implementations, increasing the microwave drive on the nonlinear oscillator that hosts the Kerr-cat qubit should, in principle, further enhance this bias. Instead, experiments reveal that above a critical drive amplitude the tunneling time - the less dominant decay channel - ceases to increase and even decreases. Here, we show that this breakdown arises from the multimode nature of the circuit implementation: specifically, the buffer mode used to control the Kerr-cat qubit can induce multiphoton resonances that sharply degrade Kerr-cat coherence if its frequency is not carefully chosen. We uncover this mechanism by retaining the full circuit nonlinearities and treating the strong drive exactly within a Floquet-Markov framework that incorporates quasidegeneracies in the Kerr-cat spectrum. Our results not only provide an explanation for the sudden reduction of the tunneling time but also demonstrate the robustness of the Kerr-cat qubit when its surrounding electromagnetic environment is carefully engineered.