  We develop an hybrid quantum-classical algorithm to solve an optimal
population transfer problem for a molecule subject to a laser pulse. The
evolution of the molecular wavefunction under the laser pulse is simulated on a
quantum computer, while the optimal pulse is iteratively shaped via a machine
learning (evolutionary) algorithm. A method to encode on the quantum computer
the n-electrons wavefunction is discussed, the circuits accomplishing its
quantum simulation are derived and the scalability in terms of number of
operations is discussed. Performance on Noisy Intermediate-Scale Quantum
devices (IBM Q X2) is provided to assess the current technological gap.
Furthermore the hybrid algorithm is tested on a quantum emulator to compare
performance of the evolutionary algorithm with standard ones. Our results show
that such algorithms are able to outperform the optimization with a downhill
simplex method and provide performance comparable to more advanced (but
quantum-computer unfriendly) algorithms such as Rabitz's.

Quantum Physics;Chemical Physics;Computational Physics