Preparation of Greenberger-Horne-Zeilinger andWstates on a one-dimensional Ising chain by global control

We study how to prepare two important types of entangled states (i.e., GHZ and W states) via global controls in closed linear Ising spin chains with nearest-neighbor couplings. To achieve the goal, we use a numerical optimization algorithm to search an optimal set of control parameters, and then analytically obtain the time-optimal solutions for a three-spin chain by a geometrical explanation on the Bloch sphere. For experimental demonstration, we also consider the most robust sequence under the realistic imperfections such as the errors of global controls and the time evolutions as well as in the numerical optimization algorithm, and experimentally implement the numerically derived robust pulse sequences in a three-spin system where the closed linear Ising spin chain is simulated by nuclear-magnetic-resonance technique. This experiment demonstrates that our scheme is feasible in realistic settings under the experimental imperfections.