  Lattice gauge theories are a fascinating and rich class of theories relating
to the most fundamental models of particle physics, and as experimental control
on the quantum level increases there is a growing interest in non-equilibrium
effects such as dynamical quantum phase transitions. To demonstrate how these
physical theories can be accessed in near-term quantum devices, we study the
dynamics of a (1+1)D U(1) quantum link model following quenches of its
mass-term. We find that the system undergoes dynamical quantum phase
transitions for all system sizes considered, even the smallest where the
dynamics can be solved analytically. We devise a gauge invariant string order
parameter whose zeros correlates with the structure of the Loschmidt amplitude,
making the order parameter useful for experimental study in near-term devices.
The zeros of the Loschmidt amplitude as well as the zeros of our order
parameter are revealed by vortices in their phases, which can be counted by a
topologically invariant winding number. With noisy intermediate scale quantum
devices in mind, we propose a class of superconducting circuits for the general
implementation of U(1) quantum link models. The principles of these circuits
can be generalized to implement other, more complicated gauge symmetries.
Furthermore, the circuit can be modularly scaled to any lattice configuration.
Simulating the circuit dynamics with realistic circuit parameters we find that
it implements the target dynamics with a steady average fidelity of $ 99.5\% $
or higher. Finally, we consider readout of the circuit using a method that
yields information about all the degrees of freedom with resonators coupled
dispersively to only a subset of them. This constitutes a direct and relatively
straightforward protocol to access both Loschmidt amplitudes and the order
parameter.
