  The spontaneous emission rate (SER) is an important figure of merit for any
quantum bit (qubit), as it can play a significant role in the control and
decoherence of the qubit. As a result, accurately characterizing the SER for
practical devices is an important step in the design of quantum information
processing devices. Here, we specifically focus on the experimentally popular
platform of a transmon qubit, which is a kind of superconducting circuit qubit.
Despite the importance of understanding the SER of these qubits, it is often
determined using approximate circuit models or is inferred from measurements on
a fabricated device. To improve the accuracy of predictions in the design
process, it is better to use full-wave numerical methods that can make a
minimal number of approximations in the description of practical systems. In
this work, we show how this can be done with a recently developed field-based
description of transmon qubits coupled to an electromagnetic environment. We
validate our model by computing the SER for devices similar to those found in
the literature that have been well-characterized experimentally. We further
cross-validate our results by comparing them to simplified lumped element
circuit and transmission line models as appropriate.
