  Understanding the collective quantum dynamics of nonequilibrium many-body
systems is an outstanding challenge in quantum science. In particular, dynamics
driven by quantum fluctuations are important for the formation of exotic
quantum phases of matter \cite{altman2023quantum}, fundamental high-energy
processes \cite{bauer2023highenergy}, quantum metrology \cite{degen2017sensing,
li2023scrambling}, and quantum algorithms \cite{ebadi2022quantum}. Here, we use
a programmable quantum simulator based on Rydberg atom arrays to experimentally
study collective dynamics across a (2+1)D Ising quantum phase transition. After
crossing the quantum critical point, we observe a gradual growth of
correlations through coarsening of antiferromagnetically ordered
domains~\cite{Samajdar2024}. By deterministically preparing and following the
evolution of ordered domains, we show that the coarsening is driven by the
curvature of domain boundaries, and find that the dynamics accelerate with
proximity to the quantum critical point. We quantitatively explore these
phenomena and further observe long-lived oscillations of the order parameter,
corresponding to an amplitude (Higgs) mode \cite{pekker2015amplitude}. These
observations offer a unique viewpoint into emergent collective dynamics in
strongly correlated quantum systems and nonequilibrium quantum processes.
