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Progress in the creation of large scale, artificial quantum coherentstructures demands the investigation of their nonequilibrium dynamics whenstrong interactions, even between remote parts, are non-perturbative. Analysisof multiparticle quantum correlations in a large system in the presence ofdecoherence and external driving is especially topical. Still, scalingbehaviour of dynamics and related emergent phenomena are not yet wellunderstood. We investigate how the dynamics of a driven system of severalquantum elements (e.g., qubits or Rydberg atoms) changes with increasing numberof elements. Surprisingly, a two-element system exhibits chaotic behaviours.For larger system sizes a highly stochastic, far from equilibrium, {\emhyperchaotic} regime emerges. Its complexity systematically scales with thesize of the system, proportionally to the number of elements. Finally, wedemonstrate that these chaotic dynamics can be efficiently controlled by aperiodic driving field. The insights provided by our results indicate thepossibility of a reduced description for the behaviour of a large quantumsystem in terms of the transitions between its qualitatively differentdynamical regimes, which are controlled by a relatively small number ofparameters, and may prove useful in the design, characterization and control oflarge artificial quantum structures.

Emergence and Control of Complex Behaviours in Driven Systems of Interacting Qubits with Dissipation