Computational modeling of decay and hybridization in superconducting circuits

We present a circuit theoretic technique for computing the complex frequencies and eigenmodes of superconducting circuits with radiative loss. We show that the transmon loss rates obtained by our method agree with the established approximation C/Re[Y] away from resonance and do not diverge near resonance. Additionally, we demonstrate that in systems with significant radiative loss, couplings between modes cannot be accurately computed if the loss is neglected. Our simulation technique is useful for designing complex superconducting quantum processors.