  The out-of-time-ordered correlators (OTOC) and the Loschmidt echo are two
measures that are now widely being explored to characterize sensitivity to
perturbations and information scrambling in complex quantum systems. Studying
few qubits systems collectively modelled as a kicked top, we solve exactly the
three- and four- qubit cases, giving analytical results for the OTOC and the
Loschmidt echo. While we may not expect such few-body systems to display
semiclassical features, we find that there are clear signatures of the
exponential growth of OTOC even in systems with as low as 4 qubits in
appropriate regimes, paving way for possible experimental measurements. We
explain qualitatively how classical phase space structures like fixed points
and periodic orbits have an influence on these quantities and how our results
compare to the large-spin kicked top model. Finally we point to a peculiar case
at the border of quantum-classical correspondence which is solvable for any
number of qubits and yet has signatures of exponential sensitivity in a
rudimentary form.
