  In the quantum simulation of lattice gauge theories, gauge symmetry can be
either fixed or encoded as a redundancy of the Hilbert space. While
gauge-fixing reduces the number of qubits, keeping the gauge redundancy can
provide code space to mitigate and correct quantum errors by checking and
restoring Gauss's law. In this work, we consider the correctable errors for
generic finite gauge groups and design the quantum circuits to detect and
correct them. We calculate the error thresholds below which the gauge-redundant
digitization with Gauss's law error correction has better fidelity than the
gauge-fixed digitization. Our results provide guidance for fault-tolerant
quantum simulations of lattice gauge theories.
