  The non-integrability of quantum systems, often associated with chaotic
behavior, is a concept typically applied to cases with a high-dimensional
Hilbert space Among different indicators signaling this behavior, the study of
the long-time oscillations of the out-of-time-ordered correlator (OTOC) appears
as a versatile tool, that can be adapted to the case of systems with a small
number of degrees of freedom. Using such an approach, we consider the
oscillations observed after the scrambling time in the measurement of OTOCs of
local operators for an Ising spin chain on a nuclear magnetic resonance quantum
simulator [J. Li,et al, Phys. Rev. X 7, 031011 (2017)]. We show that the
systematic of the OTOC oscillations describes qualitatively well, in a chain
with only 4 spins, the integrability-to-chaos transition inherited from the
infinite chain.
