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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.

Thanks!

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  • $\begingroup$ If you have some sort of symmetry like that in your simulation (where there isn't a physical constraint in the simulation that automatically imposes the symmetry), presumably you would rewrite your simulation to factor out the symmetry (so you're working with fewer qubits), and gain the saving that way. $\endgroup$
    – DaftWullie
    Apr 11, 2022 at 14:41
  • $\begingroup$ sure. That makes sense. But I'm thinking about it in the context of error mitigation. Namely, scenarios where there is a physical constraint that imposes the symmetry, and if this constraint is still broken we can infer that some error occured. In this case, perhaps it makes sense to add some redundancy with additional qubits in order to detect these errors? $\endgroup$
    – Lior
    Apr 11, 2022 at 14:47
  • $\begingroup$ I suppose that what I'm trying to say is that any errors you correct that way are the symmetry-breaking errors which are precisely the ones that would never arise if you took that into account in the design of the simulation. I agree there could be other checks that one might perform mid-simulation which are not about known symmetries and just help keep you on track. $\endgroup$
    – DaftWullie
    Apr 13, 2022 at 6:51

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Yes, this has been considered previously in just the way you described, usually considering particle number and spin conservation.

You can read more about this and find some further references on page 27 of this review paper. under "Symmetry verification".

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