Decoherence scaling transition in the dynamics of quantum information scrambling

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.