Optimal control based numerical algorithms were used to explore the minimum duration of a variety of quantum gates between the first and the last spins in a linear spin chain with identical next neighbor Ising couplings. The true SWAP gate, the planar SWAP gate and the generation of an effective direct Ising coupling between the first and the third spin were studied. Pulse sequences with shortest durations were experimentally implemented in a three-qubit NMR system. The experimental results show the accuracy and feasibility of the optimized quantum gates. (C) 2014 Elsevier B.V. All rights reserved.