Driving superconducting qubits into chaos*

Kerr parametric oscillators can operate as Kerr-cat qubits, which offer advantages towards the encoding and manipulation of error-protected quantum information. Recently, they have been implemented with the SNAIL transmon superconducting circuit, which combines Kerr nonlinearity and a squeezing drive. In this presentation, we show that when the nonlinearities and the drive are strong, the qubit melts away due to the onset of chaos. By exploring various ranges of experimentally accessible parameters, we provide an equation for the crossing line between regularity and chaos. If on the one hand chaos puts limits on the Kerr-cat qubit, on the other hand it opens up a new direction of research for superconducting circuits.