  The lattice compact Abelian Higgs model is a non-perturbative regularized
formulation of low-energy scalar quantum electrodynamics. In 1+1 dimensions,
this model can be quantum simulated using a ladder-shaped optical lattice with
Rydberg-dressed atoms (Zhang et al., Phys. Rev. Lett. 121, 223201). In this
setup, one spatial dimension is used to carry the angular momentum of the
quantum rotors. One can use truncations corresponding to spin-2 and spin-1 to
build local Hilbert spaces associated with the links of the lattice. We argue
that ladder-shaped configurable arrays of Rydberg atoms can be used for the
same purpose. We make concrete proposals involving two and three Rydberg atoms
to build one local spin-1 space (a qutrit). We show that the building blocks of
the Hamiltonian calculations are models with one and two spins. We compare
target and simulators using perturbative and numerical methods. The two-atom
setup provides an easily controllable simulator of the one-spin model while the
three-atom setup involves solving nonlinear equations. This could be tested
with current technology. We argue that near-term technology could be used to
quantum simulate models with two or more spins.
