Stacking QSE

[hametar0u]

Just following up on our conversation in #2251 , can nothing can be stacked on top of QSE? If I wanted to use the mitigate_executor function with it, then the circuit has to return a MeasurementResult type object which I don't think is the same as the density matrix. And if I were to put QSE at the back, then ZNE or something would somehow have to return a density matrix, and I don't think that's possible?

[natestemen]

If you want to stack 2 QEM techniques which require different signatures for the required executor, you can sometimes still stack them if you can convert from one type to another.

Suppose you have an executor with signature ex: circuit -> density matrix. When you apply Quantum Subspace Expansion with mitiq.qse.execute_with_qse, it will return a float. You can think of execute_with_qse(ex, -)¹ as an executor with signature circuit -> float which can then be fed into ZNE.

Footnotes

1. Where - represents the "argument" to this function. ↩