Coexistence of scrambling and stability in coupled Kerr-cat qubits

Kerr-cat qubits based on Kerr parametric oscillators (KPOs) offer robust quantum information encoding through engineered nonlinear confinement. Yet, when KPOs are coupled to implement logical operations and generate entanglement, their stability can be compromised, as the interplay between coupling and nonlinearity gives rise to complex dynamics, including signatures of chaos and information scrambling. We show that even in the presence of chaotic motion at high excitation energies, quantum information encoded in the two-qubit subspace remains protected and leakage effectively controlled, enabling the reliable implementation of XX(π/2) gates. This coexistence of scrambling and stability not only establishes KPOs as resilient platforms for analog quantum information processing but also positions them as natural simulators of quantum chaos and scrambling.