Abelian lattice gauge theory with Rydberg atoms, trapped ions and quantum computers*

We discuss the tensor network formulation of the Abelian Higgs
model on a Euclidean space-time lattice as studied in high energy physics.
We propose truncated versions of the Hamiltonian and possible implementations
with Rydberg atoms, trapped ions and quantum computers.
We report on recent understanding of the effects
of truncations and approximations by clock models and how new technology
can provide a better treatment of the critical behavior. The (very) long term
goal of the research group is to design and build a dedicated device to handle
real-time evolution for Quantum Chromodynamics.