  We investigate the performance of superconducting flux qubits for the
adiabatic quantum simulation of long distance entanglement (LDE), namely a
finite ground-state entanglement between the end spins of a quantum spin chain
with open boundary conditions. As such, LDE can be considered an elementary
precursor of edge modes and topological order. We discuss two possible
implementations which simulate open chains with uniform bulk and weak end
bonds, either with Ising or with XX nearest-neighbor interactions. In both
cases we discuss a suitable protocol for the adiabatic preparation of the
ground state in the physical regimes featuring LDE. In the first case the
adiabatic manipulation and the Ising interactions are realized using dc
currents, while in the second case microwaves fields are used to control the
smoothness of the transformation and to realize the effective XX interactions.
We demonstrate the adiabatic preparation of the end-to-end entanglement in
chains of four qubits with realistic parameters and on a relatively fast time
scale.
