Effective lumped models of distributed elements for modularity and scaling in superconducting device design

In superconducting quantum device design, finite element electromagnetic (FEM) simulations are required throughout the design process. These are both computationally intensive and time-consuming. Lumped oscillator models (LOMs) allow for modular FEM simulations of superconducting device designs that can then be combined in an effective circuit model. These lumped circuit models are easily translated into circuit Hamiltonians. However, accurately incorporating the effects of distributed elements such as transmission line resonators is a challenge.

We develop and test a higher-order effective lumped oscillator model for a coplanar waveguide resonator coupled to arbitrary loads. The LOM uses capacitances obtained from FEM simulations of individual circuit elements and numerical calculations of distributed element impedances to construct an effective lumped resonator for each distributed resonator. Importantly, our model takes into account loading on both ends of a transmission line. We show a significant improvement from the baseline LOM model in predicting the system's Hamiltonian parameters of resonant frequency, coupling to lossy elements, and coupling to other resonant modes.