  Reliable processing of quantum information for developing quantum
technologies requires precise control of out-of-equilibrium many-bodysystems.
This is a highly challenging task as the fragility of quantum states to
external perturbations increases with the system-size. Here, we report on a
series of experimental quantum simulations that quantify the sensitivity of a
controlled Hamiltonian evolution to perturbations that drive the system away
from the targeted evolution. Based on out-of-time ordered correlations, we
demonstrate that the decay-rate of the process fidelity increases with the
effective number $K$ of correlated qubits as $K^{\alpha}$. As a function of the
perturbation strength, we observe a decoherence scaling transition of the
exponent $\alpha$ between two distinct dynamical regimes. In the limiting case
below the critical perturbation strength, the exponent $\alpha$ drops sharply
below 1, and there is no inherent limit to the number of qubits that can be
controlled. This resilient quantum feature of the controlled dynamics of
quantum information is promising for reliable control of large quantum systems.
