  Simulating real-time dynamics of gauge theories represents a paradigmatic use
case to test the hardware capabilities of a quantum computer, since it can
involve non-trivial input states preparation, discretized time evolution,
long-distance entanglement, and measurement in a noisy environment. We
implement an algorithm to simulate the real-time dynamics of a few-qubit system
that approximates the Schwinger model in the framework of lattice gauge
theories, with specific attention to the occurrence of a dynamical quantum
phase transition. Limitations in the simulation capabilities on IBM Quantum are
imposed by noise affecting the application of single-qubit and two-qubit gates,
which combine in the decomposition of Trotter evolution. The experimental
results collected in quantum algorithm runs on IBM Quantum are compared with
noise models to characterize the performance in the absence of error
mitigation.
