  Progress in the creation of large scale, artificial quantum coherent
structures demands the investigation of their nonequilibrium dynamics when
strong interactions, even between remote parts, are non-perturbative. Analysis
of multiparticle quantum correlations in a large system in the presence of
decoherence and external driving is especially topical. Still, scaling
behaviour of dynamics and related emergent phenomena are not yet well
understood. We investigate how the dynamics of a driven system of several
quantum elements (e.g., qubits or Rydberg atoms) changes with increasing number
of elements. Surprisingly, a two-element system exhibits chaotic behaviours.
For larger system sizes a highly stochastic, far from equilibrium, {\em
hyperchaotic} regime emerges. Its complexity systematically scales with the
size of the system, proportionally to the number of elements. Finally, we
demonstrate that these chaotic dynamics can be efficiently controlled by a
periodic driving field. The insights provided by our results indicate the
possibility of a reduced description for the behaviour of a large quantum
system in terms of the transitions between its qualitatively different
dynamical regimes, which are controlled by a relatively small number of
parameters, and may prove useful in the design, characterization and control of
large artificial quantum structures.
