Development of an Analytical Quantum Full-Wave Solution for a Transmon Qubit in a 3D Cavity

Circuit quantum electrodynamics is one of the most promising platforms for building quantum information processors. To meet the stringent performance requirements, high-fidelity general-purpose numerical methods are increasingly needed to improve designs. Currently, there exist a limited number of methods for analyzing these systems and they suffer from problematic efficiency limitations. One challenge in developing more efficient methods is the lack of available reference data that can be generated to validate them. Here, we develop an analytical quantum full-wave solution for a transmon qubit in a 3D cavity that can validate numerical methods in the future. We start by reviewing the basics of the field-based quantization method used before showing how classical electromagnetic theories can be used to analytically evaluate all field-based parameters in our formulation. We validate our analytical solution by calculating experimentally-relevant system parameters and comparing against approaches that use numerical EM eigenmodes in their solution.