The quasi-lumped qubit model in circuit quantum electrodynamics (cQED)

The performance of a superconducting quantum device or processor rests heavily on our ability to predictively model its quantum effects at unprecedented levels of precision and optimization. Here, we revisit and generalize the hybrid classical-quantum approach to the design of circuit quantum electrodynamic structures incorporating qubits and distributed transmission-line resonators. We formulate the problem in a topological manner and use the energy-participation ratio (EPR) of the distributed resonator eigenmodes as a shortcut in quantizing the effective white-box model. We present improvements in agreement over the naive theory when compared to experimental results across 10 devices, which incorporate transmon qubits coupled to varying numbers of resonant structures.