Quench dynamics of the Schwinger model via variational quantum algorithms

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.