  Tracking the dynamics of physical systems in real time is a prime application
of digital quantum computers. Using a trapped-ion system with up to six qubits,
we simulate the real-time dynamics of a lattice gauge theory in 1+1 dimensions,
i.e., the lattice Schwinger model, and demonstrate non-perturbative effects
such as pair creation for times much longer than previously accessible. We
study the gate requirement of two formulations of the model using the
Suzuki-Trotter product formula, as well as the trade-off between errors from
the ordering of the Hamiltonian terms, the Trotter step size, and experimental
imperfections. To mitigate experimental errors, a recent symmetry-protection
protocol for suppressing coherent errors and a symmetry-inspired post-selection
scheme are applied. This work demonstrates the integrated theoretical,
algorithmic, and experimental approach that is essential for efficient
simulation of lattice gauge theories and other complex physical systems.
