  Strongly-coupled gauge theories far from equilibrium may exhibit unique
features that could illuminate the physics of the early universe and of hadron
and ion colliders. Studying real-time phenomena has proven challenging with
classical-simulation methods, but is a natural application of quantum
simulation. To demonstrate this prospect, we quantum compute non-equal time
correlation functions and perform entanglement tomography of non-equilibrium
states of a simple lattice gauge theory, the Schwinger model, using a
trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term
devices, a recently-predicted [Zache et al., Phys. Rev. Lett. 122, 050403
(2019)] dynamical quantum phase transition in this model is studied by
preparing, quenching, and tracking the subsequent non-equilibrium dynamics in
three ways: i) overlap echos signaling dynamical transitions, ii) non-equal
time correlation functions with an underlying topological nature, and iii) the
entanglement structure of non-equilibrium states, including entanglement
Hamiltonians. These results constitute the first observation of a dynamical
quantum phase transition in a lattice gauge theory on a quantum computer, and
are a first step toward investigating topological phenomena in nuclear and
high-energy physics using quantum technologies.
