  We investigate the validity of two common assumptions in the modelling of
superconducting circuits: first, that the superconducting qubits are pointlike,
and second, that the UV behaviour of the transmission line is not relevant to
the qubit dynamics. We show that in the experimentally accessible ultra-strong
coupling regime and for short (but attainable) times, the use of an inaccurate
cutoff model (such as sharp, or none at all) could introduce very significant
inaccuracies in the model's predictions.
