  With recent progress in quantum simulations of lattice-gauge theories, it is
becoming a pressing question how to reliably protect the gauge symmetry that
defines such models. In a recent work [J. C. Halimeh \textit{et al.},
arXiv:2108.02203], an experimentally feasible gauge-protection scheme has been
proposed that is based on the concept of a \textit{local pseudogenerator},
which is required to act identically to the full gauge-symmetry generator in
the target gauge sector, but not necessarily outside of it. The scheme has been
analytically and numerically shown to reliably stabilize lattice gauge theories
in the presence of perturbative errors on finite-size analog quantum-simulation
devices. In this work, through uniform matrix product state calculations, we
demonstrate the efficacy of this scheme for nonperturbative errors in analog
quantum simulators up to all accessible evolution times in the thermodynamic
limit, where it is \textit{a priori} neither established nor expected that this
scheme will succeed. Our results indicate the presence of an emergent gauge
symmetry in an adjusted gauge theory even in the thermodynamic limit, which is
beyond our analytic predictions. Additionally, we show through quantum circuit
model calculations that gauge protection with local pseudogenerators also
successfully suppresses gauge violations on finite quantum computers that
discretize time through Trotterization. Our results firm up the robustness and
feasibility of the local pseudogenerator as a viable tool for enforcing gauge
invariance in modern quantum simulators and NISQ devices.
