  We use a novel optimization procedure that includes the temporal and spatial
parameters of the pulses acting on arrays of trapped neutral atoms, to prepare
entangling gates in N-qubits systems. The spatio-temporal control allows
treating a denser array of atoms, where each pulse acts on a subset of the
qubits, potentially allowing to speed the gate operation by two orders of
magnitude by boosting the dipole-blockade between the Rydberg states. Studying
the rate of success of the algorithm under different constraints, we evaluate
the impact of the proximity of the atoms and, indirectly, the role of the
geometry of the arrays in 3 and 4-qubit systems, as well as the minimal energy
requirements and how this energy is used among the different qubits. Finally,
we characterize and classify all optimal protocols according to the mechanism
of the gate, using a quantum pathways analysis.
