Gauge theories are the backbone of our current understanding of
fundamental interactions. While some of their aspects can be
understood using established perturbative techniques, the need for a
non-perturbative framework led to the lattice formulation of gauge
theories by Wilson in 1974. Since then, numerical simulations of
lattice gauge theories have celebrated success in a plethora of
equilibrium phenomena, such as the ab initio calculation of the
low-energy hadron spectrum. However, classical simulations of gauge
theories face a major challenge when addressing real-time dynamics,
which has hampered the full understanding of many physical phenomena
including the complex thermalization during heavy-ion collisions and
the dynamics of string breaking studied at high-intensity laser
facilities. Here, we report on the experimental realization of a U(1)
lattice gauge theory on a trapped ion quantum computer. By encoding
the gauge fields in asymmetric long-range interactions between the
fermions, we are able to realize a minimal instance of Wilson’s
version of quantum electrodynamics in (1+1)-dimensions, i.e., the
Schwinger model. We investigate its real-time dynamics following a
quantum quench from the vacuum state for a broad range of masses and
electric-field couplings. Further, we experimentally quantify the
entanglement generated during the dynamics, using the logarithmic
negativity, and show that it displays qualitatively different features
in different parameter regimes, which are already appreciable for the
modest system sizes under investigation.

Joint work with M. Heyl, P. Hauke, M. Dalmonte, P. Zoller, E.
Martinez, D. Nigg, A. Erhard, P. Schindler, T. Monz, R. Blatt