  Experiments in coherent nuclear and electron magnetic resonance,and quantum
computing in general correspond to control of quantum mechanical systems,
guiding them from initial to final target states by unitary transformations.
The control inputs (pulse sequences) that accomplish these unitary
transformations should take as little time as possible so as to minimize the
effects of relaxation and decoherence and to optimize the sensitivity of the
experiments. Here, we derive a time-optimal sequences as fundamental building
blocks for synthesize unitary transformations. Such sequences can be widely
implemented on various physical systems, including the simulation of effective
Hamiltonians for topological quantum computing on spin lattices. Experimental
demonstrations are provided for a system consisting of three nuclear spins.
