Hi all,

Abstract: Quantum computers can speed up the calculation of the time
evolution of quantum states, a task that is classically hard because
just storing the wavefunction of a state of multiple particles requires
resources exponential in the number of particles. Here we present a
variational hybrid quantum-classical algorithm based on McLachlans
variational principle that approximates the time evolution of particles
moving in arbitrary potentials. We then numerically study the
performance of this algorithm on a free Gaussian wave packet in one
dimension and the scattering of a Gaussian wave packet on an Eckart
barrier. We find that for a free particle the number of parameters in
the variational form used by us can be significantly smaller than the
real dimension of the Hilber space, while for the Eckart barrier it has
to be close to the real dimension of the Hilbert space to obtain an high