Simulating long-distance entanglement in quantum spin chains by superconducting flux qubits

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 an open quantum spin chain. 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.