Measuring stabilizer eigenvalues is a fundamental part of quantum error correction. However, I was wondering if the idea of measuring a stabilizer using an ancilla could be useful in other contexts as well, specifically as an error mitigation technique. For example, when performing a NISQ algorithm, perhaps we know that in general, or during specific steps, the state must obey some symmetry property or have a well defined parity. (What comes to mind is e.g when performing a simulation of an electronic system, we know that the wavefunction must be anti-symmetric to particle exchange). Then, we could insert stabilizer measurements in specific places in the circuit to perform error detection or perhaps even correction.
Is that something that has been considered in the past? If so, I'd really appreciate if someone could post a reference to existing works. If not, I'd be happy to understand if there's some fundamental reason why this wouldn't be possible or is otherwise a clearly bad idea.