  We show that optimal control of the electron dynamics is able to prepare
molecular ground states, within chemical accuracy, with evolution times
approaching the bounds imposed by quantum mechanics. We propose a specific
parameterization of the molecular evolution only in terms of interaction
already present in the molecular Hamiltonian. Thus, the proposed method solely
utilizes quantum simulation routines, retaining their favourable scalings. Due
to the intimate relationships between variational quantum algorithms and
optimal control we compare, when possible, our results with state-of-the-art
methods in literature. We found that the number of parameters needed to reach
chemical accuracy and algorithmic scaling are in line with compact adaptive
strategies to build variational ansatze. The algorithm, which is also suitable
for quantum simulators, is implemented emulating a digital quantum processor
(up to 16 qubits) and tested on different molecules and geometries spanning
different degrees of electron correlation.
