  Relaxation to a thermal state is the inevitable fate of non-equilibrium
interacting quantum systems without special conservation laws. While
thermalization in one-dimensional (1D) systems can often be suppressed by
integrability mechanisms, in two spatial dimensions thermalization is expected
to be far more effective due to the increased phase space. In this work we
propose a general framework for escaping or delaying the emergence of the
thermal state in two-dimensional (2D) arrays of Rydberg atoms via the mechanism
of quantum scars, i.e. initial states that fail to thermalize. The suppression
of thermalization is achieved in two complementary ways: by adding local
perturbations or by adjusting the driving Rabi frequency according to the local
connectivity of the lattice. We demonstrate that these mechanisms allow to
realize robust quantum scars in various two-dimensional lattices, including
decorated lattices with non-constant connectivity. In particular, we show that
a small decrease of the Rabi frequency at the corners of the lattice is crucial
for mitigating the strong boundary effects in two-dimensional systems. Our
results identify synchronization as an important tool for future experiments on
two-dimensional quantum scars.
