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 a system of two resonators coupled to a common Purcell filter exhibits a pattern of hybridization that cannot be explained by a hierarchy of couplings and detunings. This is due to the significant influence of radiative loss on the mode couplings. As a result, it is necessary to include radiative boundary conditions even in simulations of coherent dynamics. Our simulation technique is useful for designing complex circuit quantum electrodynamic systems.