Pato and Klco (2602.22121) study what happens when you try to use a system's built-in symmetries for error correction in quantum simulations of electrodynamics. Gauss's law constrains how electric fields can be configured — violating it means you've left the physical Hilbert space. So you can use Gauss's law violations as error syndromes: detect them, fix them, stay physical.
Except there's a threshold. Above a physical error rate of p = 0.277, using the symmetry-based correction makes decoherence faster than doing nothing at all.
The mechanism is subtle. Gauss's law error correction (GLQEC) can achieve lower single-round logical error rates than a generic quantum error correction code. It wins the battle. But it loses the war: under repeated correction rounds, the system mixes toward the maximally mixed state faster than without correction. The symmetry-based code has fewer degrees of freedom to absorb errors, so the errors it can't fix accumulate more destructively.
There's an additional constraint: GLQEC requires periodic boundary conditions on the electric field. This restricts the space of simulations you can even attempt. The symmetry that lets you correct errors also limits the physics you can study.
The parallel to non-quantum systems is direct. Any time you exploit a conservation law for error detection, you're assuming the conservation law holds more reliably than the dynamics you're simulating. Below the threshold, that assumption pays off. Above it, the correction mechanism itself becomes a channel for correlated errors. The fix becomes the disease — not through some exotic mechanism, but through the ordinary arithmetic of error accumulation. Symmetry-based correction is efficient precisely because it leverages structure, but that leverage amplifies failures when the structure is itself compromised.