  Variational Monte Carlo (VMC) methods are used to sample classically from
distributions corresponding to quantum states which have an efficient classical
description. VMC methods are based on performing a number of steps of a Markov
chain starting with samples from a simple initial distribution. Here we propose
replacing this initial distribution with samples produced using a quantum
computer, for example using the variational quantum eigensolver (VQE). We show
that, based on the use of initial distributions generated by numerical
simulations and by experiments on quantum hardware, convergence to the target
distribution can be accelerated compared with classical samples; the energy can
be reduced compared with the energy of the state produced by VQE; and VQE
states produced by small quantum computers can be used to accelerate large
instances of VMC. Quantum-enhanced VMC makes minimal requirements of the
quantum computer and offers the prospect of accelerating classical methods
using noisy samples from near-term quantum computers which are not yet able to
accurately represent ground states of complex quantum systems.
