  Simulations and analytical calculations that aim to describe flux-tunable
transmons are usually based on effective models of the corresponding
lumped-element model. However, when a control pulse is applied, in most cases
it is not known how much the predictions made with the effective models deviate
from the predictions made with the original lumped-element model. In this work
we compare the numerical solutions of the time-dependent Schr\"odinger equation
for both the effective and the lumped-element models, for microwave and
unimodal control pulses (external fluxes). These control pulses are used to
model single-qubit (X) and two-qubit gate (Iswap and Cz) transitions. First, we
derive a non-adiabatic effective Hamiltonian for a single flux-tunable transmon
and compare the pulse response of this model to the one of the corresponding
circuit Hamiltonian. Here we find that both models predict similar outcomes for
similar control pulses. Then, we study how different approximations affect
single-qubit (X) and two-qubit gate (Iswap and Cz) transitions in two different
two-qubit systems. For this purpose we consider three different systems in
total: a single flux-tunable transmon and two two-qubit systems. In summary, we
find that a series of commonly applied approximations (individually and/or in
combination) can change the response of a system substantially, when a control
pulse is applied.
