  This work aims at giving Trotter errors in digital quantum simulation (DQS)
of collective spin systems an interpretation in terms of quantum chaos of the
kicked top. In particular, for DQS of such systems, regular dynamics of the
kicked top ensures convergence of the Trotterized time evolution, while chaos
in the top, which sets in above a sharp threshold value of the Trotter step
size, corresponds to the proliferation of Trotter errors. We show the
possibility to analyze this phenomenology in a wide variety of experimental
realizations of the kicked top, ranging from single atomic spins to trapped-ion
quantum simulators which implement DQS of all-to-all interacting spin-1/2
systems. These platforms thus enable in-depth studies of Trotter errors and
their relation to signatures of quantum chaos, including the growth of
out-of-time-ordered correlators.
