  We study multiple-spin coherence transfers in linear Ising spin chains with
nearest neighbor couplings. These constitute a model for efficient information
transfers in future quantum computing devices and for many multi-dimensional
experiments for the assignment of complex spectra in nuclear magnetic resonance
spectroscopy. We complement prior analytic techniques for multiple-spin
coherence transfers with a systematic numerical study where we obtain strong
evidence that a certain analytically-motivated family of restricted controls is
sufficient for time-optimality. In the case of a linear three-spin system,
additional evidence suggests that prior analytic pulse sequences using this
family of restricted controls are time-optimal even for arbitrary local
controls. In addition, we compare the pulse sequences for linear Ising spin
chains to pulse sequences for more realistic spin systems with additional
long-range couplings between non-adjacent spins. We experimentally implement
the derived pulse sequences in three and four spin systems and demonstrate that
they are applicable in realistic settings under relaxation and experimental
imperfections-in particular-by deriving broadband pulse sequences which are
robust with respect to frequency offsets.
