  Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties
of molecular and condensed matter systems. The quality of this procedure is
based on accurate electronic structure calculations. The development of quantum
processors has shown great potential for the efficient evaluation of accurate
ground and excited state energies of molecular systems, opening up new avenues
for molecular dynamics simulations. In this work we address the use of
variational quantum algorithms for the calculation of accurate atomic forces to
be used in AIMD. In particular, we provide solutions for the alleviation of the
statistical noise associated to the measurements of the expectation values of
energies and forces, as well as schemes for the mitigation of the hardware
noise sources (in particular, gate infidelities, qubit decoherence and readout
errors). Despite the relative large error in the calculation of the potential
energy, our results show that the proposed algorithms can provide reliable MD
trajectories in the microcanonical (constant energy) ensemble. Further,
exploiting the intrinsic noise arising from the quantum measurement process, we
also propose a Langevin dynamics algorithm for the simulation of canonical,
i.e., constant temperature, dynamics. Both algorithms (microcanonical and
canonical) are applied to the simulation of simple molecular systems such as H2
and H3+. Finally, we also provide results for the dynamics of H2 obtained with
IBM quantum computer ibmq_athens.
