Drive-induced renormalization of Kerr nonlinearity in superconducting circuits

Josephson-junction-based amplifiers are now ubiquitously used in high-fidelity qubit readout. In a three-wave mixing parametric amplifier, a cancelation of the Kerr interaction is required. In satisfying this requirement, an important limitation is that available theory does not fully explain the dependence of the Kerr nonlinearity on drive power. We propose a perturbative expansion based on unitary transformations to calculate drive-induced corrections to Kerr interactions, with possible applications to current experiments.