This paper explores the use of gauge redundancy in lattice gauge theories for quantum error correction and mitigation. The authors design quantum circuits to detect and correct errors, focusing on generic finite gauge groups. They calculate the error thresholds below which gauge-redundant digitization with Gauss's law error correction outperforms gauge-fixed digitization in terms of fidelity. The study provides guidance for fault-tolerant quantum simulations of lattice gauge theories, highlighting the advantages of maintaining gauge redundancy for error correction and mitigation. The results are applicable to both Abelian and non-Abelian gauge groups, and the authors derive explicit error rates for specific groups like \(\mathbb{Z}_N\) and \(\mathbb{Q}_8\). The findings suggest that gauge redundancy can enhance the robustness of quantum simulations by preserving symmetry and enabling more effective error correction.This paper explores the use of gauge redundancy in lattice gauge theories for quantum error correction and mitigation. The authors design quantum circuits to detect and correct errors, focusing on generic finite gauge groups. They calculate the error thresholds below which gauge-redundant digitization with Gauss's law error correction outperforms gauge-fixed digitization in terms of fidelity. The study provides guidance for fault-tolerant quantum simulations of lattice gauge theories, highlighting the advantages of maintaining gauge redundancy for error correction and mitigation. The results are applicable to both Abelian and non-Abelian gauge groups, and the authors derive explicit error rates for specific groups like \(\mathbb{Z}_N\) and \(\mathbb{Q}_8\). The findings suggest that gauge redundancy can enhance the robustness of quantum simulations by preserving symmetry and enabling more effective error correction.