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, I provide a quantitative comparison between the adiabatic and variational methods on digital quantum simulators with respect to required quantum resources, namely the depth of the circuit and the number of two-qubit quantum gates. Moreover, several methods for speeding the convergence of variational methods will be introduced which can simplify their simulation on near-term quantum simulators.
In addition to the simulation of the ground state, the quantum simulators can be used for capturing the properties of non-equilibrium dynamics in many-body systems. In the second part of the talk, I present a recent experiment on a 12-qubit super conducting quantum simulator for characterizing the many-body localization transition. Finally, we discuss the verification methods for certifying certain class of quantum simulators.

Abolfazl Bayat is a professor of Physics at the Institute of Fundamental and Frontier Sciences in University of Electronic Science and Technology of China  in Chengdu. After completing his PhD in 2008 from Sharif University of Technology in Iran, he did his postdocs at University College London (2008-2011 and 2013-2017) and University of Ulm in Germany (2011-2013). The research interest of Prof. Bayat includes: quantum simulation, quantum sensing and many-body physics.