  Arrays of Rydberg atoms are a powerful platform to realize
strongly-interacting quantum many-body systems. A common Rydberg Hamiltonian is
free of the sign problem, meaning that its equilibrium properties are amenable
to efficient simulation by quantum Monte Carlo (QMC). In this paper, we develop
a Stochastic Series Expansion QMC algorithm for Rydberg atoms interacting on
arbitrary lattices. We describe a cluster update that allows for the efficient
sampling and calculation of physical observables for typical experimental
parameters, and show that the algorithm can reproduce experimental results on
large Rydberg arrays in one and two dimensions.
