  In recent years there has been growing interest in characterizing the
complexity of quantum evolutions of interacting many-body systems. When the
dynamics is governed by a time-independent Hamiltonian, Krylov complexity has
emerged as a powerful tool. For unitary evolutions like kicked systems or
Trotterized dynamics, a similar formulation based on the Arnoldi approach has
been proposed (P. Suchsland, R. Moessner, and P. W. Claeys, (2023),
arXiv:2308.03851). In this work, we show that this formulation is robust for
observing the transition from integrability to chaos in both autonomous and
kicked systems. Examples from random matrix theory and spin chains are shown in
this paper.
