Quantum error thresholds for gauge-redundant digitizations of lattice field theories

In the quantum simulation of lattice gauge theories, gauge symmetry can be either fixed or encoded as a redundancy of the Hilbert space. While fixing the gauge reduces the required number of qubits, keeping the gauge redundancy can provide space to mitigate and correct certain quantum errors by checking and restoring Gauss's law. In this talk, treating the gauge redundancy as approximate error correction codes, I will present the correctable errors for generic finite gauge groups and the quantum circuits to detect and correct them. Noise thresholds are obtained below which the gauge-redundant digitization combined with error correction has better fidelity than the gauge-fixed digitization.