  We present a hybrid classical-quantum algorithm to solve optimization
problems in current quantum computers, whose basic idea is to assist
variational quantum eigensolvers (VQE) with adiabatic change of the
Hamiltonian. The rational for this new algorithm is to circumvent the problem
of facing very small gradients in the classical optimization piece of a VQE,
while being able to run in current hardware efficient devices. A discrete
concatenation of VQEs adapted to interpolating Hamiltonians provides a method
to keep the quantum state always close to a path faithfully directed to find
the final solution. We benchmark this Adiabatically Assisted Variational
Quantum Eigensolver (AAVQE) on quantum Hamiltonians and hard classical
problems, for which our approach shows fast convergence.
