**Abstract: **Digital quantum computers are expected to be universal, namely being able to simulate any quantum state and process. In the era of Noisy Intermediate-Scale Quantum (NISQ) computing the simulators are still far from being perfect and several errors may occur in initialization, manipulation and readout. Therefore, finding the most efficient way for simulating the ground state on a NISQ simulator is of huge interest. Traditionally, adiabatic theorem has been proposed to slowly evolve a simple Hamiltonian, while the system is initialized in its ground state, to the Hamiltonian of interest. If the evolution is slow enough the system always remain the ground state of the instant Hamiltonian and at the end of the evolution the target state is achieved. However, the time needed for the adiabatic evolution grows as the energy gap of the system goes down by increasing the system size. In recent years, Variational Quantum Eigensolver (VQE) has been proposed for preparing the ground state of many-body systems. In VQE a quantum state is encoded by a few parameters and is varied until its average energy converges to its minimum. The converged quantum state is the ground state of the Hamiltonian. In this talk, we compare the realization of these two algorithms, namely the adiabatic evolution and the VQE, on a digital quantum simulator. We show that VQE can achieve the ground state with requiring far less gates than the adiabatic evolution. Thus, in the NISQ era, where simulators are still noisy, finding efficient designs for VQE circuits will be one of the main objectives of quantum simulation.

**Brief Introduction: **Prof. Abolfazl Bayat is a Professor of Physics from University of Electronic Science and Technology of China. His research topic includes: Many-Body Physics at and out of Equilibrium, Quantum Sensing, ManyBody Localization, Quantum Simulators.