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We characterize the set of optimal protocols for two-qubit entangling gatesthrough a mechanism analysis based on quantum pathways, which allows us tocompare and rank the different solutions. As an example of a flexible platformwith a rich landscape of protocols, we consider trapped neutral atoms excitedto Rydberg states by different pulse sequences that extend over several atomicsites, optimizing both the temporal and the spatial features of the pulses.Studying the rate of success of the algorithm under different constraints, weanalyze the impact of the proximity of the atoms on the nature and quality ofthe optimal protocols. We characterize in detail the features of the solutionsin parameter space, showing some striking correlations among the set ofparameters. Together with the mechanism analysis, the spatio-temporal controlallows us to select protocols that operate under mechanisms by design, likefinding needles in the haystack.

Finding, mapping and classifying optimal protocols for two-qubit entangling gates