  We investigate the real-time dynamics of the $(1+1)$-dimensional U(1) gauge
theory known as the Schwinger model via variational quantum algorithms.
Specifically, we simulate quench dynamics in the presence of an external
electric field. First, we use a variational quantum eigensolver to obtain the
ground state of the system in the absence of an external field. With this as
the initial state, we perform real-time evolution under an external field via a
fixed-depth, parameterized circuit whose parameters are updated using
McLachlan's variational principle. We use the same Ansatz for initial state
preparation and time evolution, by which we are able to reduce the overall
circuit depth. We test our method with a classical simulator and confirm that
the results agree well with exact diagonalization.
