High-fidelity general-purpose numerical methods are increasingly needed to
improve superconducting circuit quantum information processor performance. One
challenge in developing such numerical methods is the lack of reference data to
validate them. To address this, we have designed a 3D system where all
electromagnetic properties needed in a quantum analysis can be evaluated using
analytical techniques from classical electromagnetic theory. Here, we review
the basics of our field-based quantization method and then use these techniques
to create the first-ever analytical quantum full-wave solution for a
superconducting circuit quantum device. Specifically, we analyze a coaxial-fed
3D waveguide cavity with and without transmon quantum bits inside the cavity.
We validate our analytical solutions by comparing them to numerical methods in
evaluating single photon interference and computing key system parameters
related to controlling quantum bits. In the future, our analytical solutions
can be used to validate numerical methods, as well as build intuition about
important quantum effects in realistic 3D devices.Comment: 14 pages, 11 figure