  The kicked top is one of the paradigmatic models in the study of quantum
chaos~[F.~Haake et al., \emph{Quantum Signatures of Chaos (Springer Series in
Synergetics vol 54)} (2018)]. Recently it has been shown that the onset of
quantum chaos in the kicked top can be related to the proliferation of Trotter
errors in digital quantum simulation (DQS) of collective spin systems.
Specifically, the proliferation of Trotter errors becomes manifest in
expectation values of few-body observables strongly deviating from the target
dynamics above a critical Trotter step, where the spectral statistics of the
Floquet operator of the kicked top can be predicted by random matrix theory. In
this work, we study these phenomena in the framework of Hamiltonian learning
(HL). We show how a recently developed Hamiltonian learning protocol can be
employed to reconstruct the generator of the stroboscopic dynamics, i.e., the
Floquet Hamiltonian, of the kicked top. We further show how the proliferation
of Trotter errors is revealed by HL as the transition to a regime in which the
dynamics cannot be approximately described by a low-order truncation of the
Floquet-Magnus expansion. This opens up new experimental possibilities for the
analysis of Trotter errors on the level of the generator of the implemented
dynamics, that can be generalized to the DQS of quantum many-body systems in a
scalable way. This paper is in memory of our colleague and friend Fritz Haake.

Quantum Physics