  Simulations of lattice gauge theories on noisy quantum hardware inherently
suffer from violations of the gauge symmetry due to coherent and incoherent
errors of the underlying physical system that implements the simulation. These
gauge violations cause the simulations to become unphysical requiring the
result of the simulation to be discarded. We investigate an active correction
scheme that relies on detecting gauge violations locally and subsequently
correcting them by dissipatively driving the system back into the physical
gauge sector. We show that the correction scheme not only ensures the
protection of the gauge symmetry, but it also leads to a longer validity of the
simulation results even within the gauge-invariant sector. Finally, we discuss
further applications of the scheme such as preparation of the many-body ground
state of the simulated system.
