  The study of quantum heat transport in superconducting circuits is
significant for further understanding the connection between quantum mechanics
and thermodynamics, and for possible applications for quantum information. The
first experimental realisations of devices demonstrating photonic heat
transport mediated by a qubit have already been designed and measured.
Motivated by the analysis of such experimental results, and for future
experimental designs, we numerically evaluate the photonic heat transport of
qubit-resonator devices in the linear circuit regime through electromagnetic
simulations using Sonnet software, and compare with microwave circuit theory.
We show that the method is a powerful tool to calculate heat transport and
predict unwanted parasitic resonances and background.
