  Superconducting qubits are one of the most mature platforms for quantum
computing, but significant performance improvements are still needed. To
improve the engineering of these systems, 3D full-wave computational
electromagnetics analyses are increasingly being used. Unfortunately, existing
analysis approaches often rely on full-wave simulations using eigenmode solvers
that are typically cumbersome, not robust, and computationally prohibitive if
devices with more than a few qubits are to be analyzed. To improve the
characterization of superconducting circuits while circumventing these
drawbacks, this work begins the development of an alternative framework that we
illustrate in the context of evaluating the qubit-qubit exchange coupling rate
between transmon qubits. This is a key design parameter that determines the
entanglement rate for fast multi-qubit gate performance and also affects
decoherence sources like qubit crosstalk. Our modeling framework uses a
field-based formalism in the context of macroscopic quantum electrodynamics,
which we use to show that the qubit-qubit exchange coupling rate can be related
to the electromagnetic dyadic Green's function linking the qubits together. We
further show how the quantity involving the dyadic Green's function can be
related to the impedance response of the system that can be efficiently
computed with classical computational electromagnetics tools. We demonstrate
the validity and efficacy of this approach by simulating four practical
multi-qubit superconducting circuits and evaluating their qubit-qubit exchange
coupling rates. We validate our results against a 3D numerical diagonalization
method and against experimental data where available. We also demonstrate the
impact of the qubit-qubit exchange coupling rate on qubit crosstalk by
simulating a multi-coupler device and identifying operating points where the
qubit crosstalk becomes zero.
