Experimental digital quantum simulation of temporal-spatial dynamics of interacting fermion system

Efficient simulations of many-body quantum systems are generally difficult on classical computers due to the exponential resource growth with the system size, while quantum computer has been proved to complete the same task effectively. In this article, we studied quantum algorithms for digital simulation of the dynamics of interacting quantum systems in real space. As an illustrative example, we concentrated on a digital quantum simulation algorithm for a two-fermion system with Coulomb interaction. We experimentally realized our algorithm on a three-qubit NMR device, and interesting phenomena such as the moving toward or against each other of particles under attractive or repulsive interaction have been clearly observed. This experiment demonstrated the very promising potential of quantum computers, even of small scale, to address the simulation of complex quantum systems.