  We present the meta-VQE, an algorithm capable to learn the ground state
energy profile of a parametrized Hamiltonian. By training the meta-VQE with a
few data points, it delivers an initial circuit parametrization that can be
used to compute the ground state energy of any parametrization of the
Hamiltonian within a certain trust region. We test this algorithm with a XXZ
spin chain, an electronic H$_{4}$ Hamiltonian and a single-transmon quantum
simulation. In all cases, the meta-VQE is able to learn the shape of the energy
functional and, in some cases, resulted in improved accuracy in comparison to
individual VQE optimization. The meta-VQE algorithm introduces both a gain in
efficiency for parametrized Hamiltonians, in terms of the number of
optimizations, and a good starting point for the quantum circuit parameters for
individual optimizations. The proposed algorithm proposal can be readily mixed
with other improvements in the field of variational algorithms to shorten the
distance between the current state-of-the-art and applications with quantum
advantage.
