  Ultracold molecules trapped in optical tweezers show great promise for the
implementation of quantum technologies and precision measurements. We study a
prototypical scenario where two interacting polar molecules placed in separate
traps are controlled using an external electric field. This, for instance,
enables a quantum computing scheme in which the rotational structure is used to
encode the qubit states. We estimate the typical operation timescales needed
for state engineering to be in the range of few microseconds. We further
underline the important role of the spatial structure of the two-body states,
with the potential for significant gate speedup employing trap-induced
resonances.
