Flux-based three-dimensional electrodynamic modeling approach to superconducting circuits and materials

Modeling the behavior of superconducting electronic circuits containing Josephson junctions is crucial for the design of superconducting information processors and devices. In this paper, we introduce DEC-QED, a computational approach for modeling the electrodynamics of superconducting electronic circuits containing Josephson junctions in arbitrary three-dimensional electromagnetic environments. DEC-QED captures the nonlinear response and induced currents in BCS superconductors and accurately captures phenomena such as the Meissner effect, flux quantization, and Josephson effects. Using a spatial coarse-graining formulation based on discrete exterior calculus (DEC), DEC-QED can accurately simulate transient and long-time dynamics in superconductors. Finally, the expression of the entire electrodynamic problem in terms of the gauge-invariant flux field and charges makes the resulting classical field theory suitable for second quantization.