Fundamental Limits to Cat Code Qubits from Chaos-Assisted Tunneling

We show that chaos-assisted tunneling (CAT) imposes an intrinsic limit to the protection of Kerr-cat qubits. In the static effective description, tunneling between the quasidegenerate cat states can be exponentially suppressed, ensuring long lifetimes. However, our Floquet analysis reveals that when the nonlinearities increase, chaotic states mediate tunneling between the cat states, producing large quasienergy splittings. We compute tunneling rates using both full quantum simulations and semiclassical WKB theory, finding quantitative agreement and confirming that the splittings are directly linked to chaos. These results provide the first evidence of CAT in the Kerr-cat qubit and demonstrate that chaos sets a fundamental bound on the coherence of dynamically protected superconducting qubits.