  Lattice gauge theories, which originated from particle physics in the context
of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to
further develop quantum information technologies. While one long-term goal is
the reliable quantum simulation of currently intractable aspects of QCD itself,
lattice gauge theories also play an important role in condensed matter physics
and in quantum information science. In this way, lattice gauge theories provide
both motivation and a framework for interdisciplinary research towards the
development of special purpose digital and analog quantum simulators, and
ultimately of scalable universal quantum computers. In this manuscript, recent
results and new tools from a quantum science approach to study lattice gauge
theories are reviewed. Two new complementary approaches are discussed: first,
tensor network methods are presented - a classical simulation approach -
applied to the study of lattice gauge theories together with some results on
Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the
implementation of lattice gauge theory quantum simulators in different quantum
hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting
circuits. Finally, the first proof-of-principle trapped ions experimental
quantum simulations of the Schwinger model are reviewed.
