  One of the key applications for the emerging quantum simulators is to emulate
the ground state of many-body systems, as it is of great interest in various
fields from condensed matter physics to material science. Traditionally, in an
analog sense, adiabatic evolution has been proposed to slowly evolve a simple
Hamiltonian, initialized in its ground state, to the Hamiltonian of interest
such that the final state becomes the desired ground state. Recently,
variational methods have also been proposed and realized in quantum simulators
for emulating the ground state of many-body systems. Here, we first provide a
quantitative comparison between the adiabatic and variational methods with
respect to required quantum resources on digital quantum simulators, namely the
depth of the circuit and the number of two-qubit quantum gates. Our results
show that the variational methods are less demanding with respect to these
resources. However, they need to be hybridized with a classical optimization
which can converge slowly. Therefore, as the second result of the paper, we
provide two different approaches for speeding the convergence of the classical
optimizer by taking a good initial guess for the parameters of the variational
circuit. We show that these approaches are applicable to a wide range of
Hamiltonian and provide significant improvement in the optimization procedure.
