  Optimally-shaped electromagnetic fields have the capacity to coherently
control the dynamics of quantum systems and thus offer a promising means for
controlling molecular transformations relevant to chemical, biological, and
materials applications. Currently, advances in this area are hindered by the
prohibitive cost of the quantum dynamics simulations needed to explore the
principles and possibilities of molecular control. However, the emergence of
nascent quantum-computing devices suggests that efficient simulations of
quantum dynamics may be on the horizon. In this article, we study how quantum
computers could be employed to design optimally-shaped fields to control
molecular systems. We introduce a hybrid algorithm that utilizes a quantum
computer for simulating the field-induced quantum dynamics of a molecular
system in polynomial time, in combination with a classical optimization
approach for updating the field. Qubit encoding methods relevant for molecular
control problems are described, and procedures for simulating the quantum
dynamics and obtaining the simulation results are discussed. Numerical
illustrations are then presented that explicitly treat paradigmatic vibrational
and rotational control problems, and also consider how optimally-shaped fields
could be used to elucidate the mechanisms of energy transfer in
light-harvesting complexes. Resource estimates, as well as a numerical
assessment of the impact of hardware noise and the prospects of near-term
hardware implementations, are provided for the latter task.
