A general characterization method for nonlinearities in superconducting circuits

Detailed knowledge of nonlinearity in superconducting microwave circuits is required for the optimal control of their quantum state. We present a general method to precisely characterize this nonlinearity to very high order. Our method is based on intermodulation spectroscopy at microwave frequencies and does not require DC-connection or DC-measurement of an on-chip reference structure. We give a theoretical derivation of the method and we validate it by reconstructing a known nonlinearity from simulated data. We experimentally demonstrate the reconstruction of the unknown nonlinear current-phase relation of a microwave resonator with superconducting nanowires.