Quantum chaos and quantum phase transitions in Kerr parametric oscillators

Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers. But more than qubits, they are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. We show that on the same Kerr parametric oscillator implemented with driven SNAIL transmon superconducting circuits, one can either simulate excited state quantum phase transitions (ESQPTs) or study quantum chaos. ESQPTs take place in the regime where Kerr-cat qubits are generated, while chaos sets in when the nonlinearities and drive become strong. As the parameters are changed from one limit to the other, perturbative expansions used to derive static effective models cease to capture all the relevant physics of the original driven system.