In this article we investigate the real-time dynamics in the $(1+1)$-dimensional $U(1)$ gauge theory called the Schwinger model by using variational quantum algorithms.
Specifically, we first prepare the ground state of the Hamiltonian without external electric field via the variational quantum eigensolver, and then perform real-time evolution under the Hamiltonian in the presence of the external field using the variational quantum simulation method.
The same ansatz is used for both algorithms which reduces the overall depth of the quantum circuit.
We test our protocol by using a noiseless statevector simulator and confirm that results from the quantum algorithms are consistent with those obtained by exact diagonalization.
This article summarizes our previous work [1].