  Low frequency perturbations at the boundary of critical quantum chains can be
understood in terms of the sequence of boundary conditions imposed by them, as
has been previously demonstrated in the Ising and related fermion models. Using
extensive numerical simulations, we explore the scaling behavior of the
Loschmidt echo under longitudinal field perturbations at the boundary of a
critical $\mathbb{Z}_3$ Potts model. We show that at times much larger than the
relaxation time after a boundary quench, the Loschmidt-echo has a power-law
scaling as expected from interpreting the quench as insertion of boundary
condition changing operators. Similar scaling is observed as a function of
time-period under a low frequency square-wave pulse. We present numerical
evidence which indicate that under a sinusoidal or triangular pulse, scaling
with time period is modified by Kibble-Zurek effect, again similar to the case
of the Ising model. Results confirm the validity, beyond the Ising model, of
the treatment of the boundary perturbations in terms of the effect on boundary
conditions.
