  The quantum compass model consists of a two-dimensional square spin lattice
where the orientation of the spin-spin interactions depends on the spatial
direction of the bonds. It has remarkable symmetry properties and the ground
state shows topological degeneracy. The implementation of the quantum compass
model in quantum simulation setups like ultracold atoms and trapped ions is far
from trivial, since spin interactions in those sytems typically are independent
of the spatial direction. Ising spin interactions, on the contrary, can be
induced and controlled in atomic setups with state-of-the art experimental
techniques. In this work, we show how the quantum compass model on a
rectangular lattice can be simulated by the use of the photon-assisted
tunneling induced by periodic drivings on a quantum Ising spin model. We
describe a procedure to adiabatically prepare one of the doubly-degenerate
ground states of this model by adiabatically ramping down a transverse magnetic
field, with surprising differences depending on the parity of the lattice size.
Exact diagonalizations confirm the validity of this approach for small
lattices. Specific implementations of this scheme are presented with ultracold
atoms in optical lattices in the Mott insulator regime, as well as with Rydberg
atoms.
