Numerically modeling the Hamiltonian of a microwave-driven superconducting circuit

Modeling the time-dependent Hamiltonian of a driven Josephson circuit is imperative to superconducting quantum computation. So far, static circuit Hamiltonians have been modeled by numerical schemes such as BBQ or EPR. In contrast, numerical modeling of the driven Hamiltonian in the presence of external voltage or flux modulation, without relying on a lumped-element circuit model, has been largely unexplored. Here, we present a numerical method that leverages finite-element simulation to obtain the low-energy time-dependent Hamiltonian of a multimode and multi-junction Josephson device with complex geometry in the presence of external drives. Our scheme serves as a promising toolbox for characterizing the driven properties of realistic circuit devices in complicated electromagnetic environments - a task not typically amenable to standard lumped-element circuit analysis. Consequently, our technique should have wide application to the optimization of various circuit designs.