The paper investigates the collective dynamics of a (2+1)D Ising quantum phase transition using a programmable quantum simulator based on Rydberg atom arrays. After crossing the quantum critical point, the system exhibits a gradual growth of correlations through the coarsening of antiferromagnetically ordered domains. The dynamics are driven by the curvature of domain boundaries, and they accelerate as the system approaches the critical point. The authors also observe long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode. These findings provide insights into the emergent collective dynamics in strongly correlated quantum systems and nonequilibrium quantum processes. The experimental results are supported by numerical simulations, which reveal that the observed oscillations can be understood as a collective excitation of the order parameter, consistent with Landau theory. The study highlights the importance of quantum fluctuations and the curvature-driven nature of coarsening dynamics in systems with a nonconserved order parameter.The paper investigates the collective dynamics of a (2+1)D Ising quantum phase transition using a programmable quantum simulator based on Rydberg atom arrays. After crossing the quantum critical point, the system exhibits a gradual growth of correlations through the coarsening of antiferromagnetically ordered domains. The dynamics are driven by the curvature of domain boundaries, and they accelerate as the system approaches the critical point. The authors also observe long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode. These findings provide insights into the emergent collective dynamics in strongly correlated quantum systems and nonequilibrium quantum processes. The experimental results are supported by numerical simulations, which reveal that the observed oscillations can be understood as a collective excitation of the order parameter, consistent with Landau theory. The study highlights the importance of quantum fluctuations and the curvature-driven nature of coarsening dynamics in systems with a nonconserved order parameter.