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.
@article{arxiv.2007.00368,
title = {Quantum optimal control with quantum computers: an hybrid algorithm featuring machine learning optimization},
author = {Davide Castaldo and Marta Rosa and Stefano Corni},
journal= {arXiv preprint arXiv:2007.00368},
year = {2021}
}