  We characterize the set of optimal protocols for two-qubit entangling gates
through a mechanism analysis based on quantum pathways, which allows us to
compare and rank the different solutions. As an example of a flexible platform
with a rich landscape of protocols, we consider trapped neutral atoms excited
to Rydberg states by different pulse sequences that extend over several atomic
sites, optimizing both the temporal and the spatial features of the pulses.
Studying the rate of success of the algorithm under different constraints, we
analyze the impact of the proximity of the atoms on the nature and quality of
the optimal protocols. We characterize in detail the features of the solutions
in parameter space, showing some striking correlations among the set of
parameters. Together with the mechanism analysis, the spatio-temporal control
allows us to select protocols that operate under mechanisms by design, like
finding needles in the haystack.
