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2

You can use stim for this, although you do have to write the stabilizer projection procedure for yourself. Write some methods to project a system into the +1 eigenstate of several stabilizers: from typing import List import stim def find_compatible_tableau(stabilizers: List[stim.PauliString]) -> stim.Tableau: num_qubits = max(len(e) for e in ...

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I'm not sure how possible what you described is. I think the best you can possibly do is to project into the $n$ qubit symmetric space by applying $$\text{SymmetricProjector}(n) = \sum_{k=0}^{n} \left|{n \atop k}\right\rangle\left\langle{n \atop k}\right|$$ where the "n choose k state" is the superposition of all n-bit numbers with k bits set: \...

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I believe what you try to do is impossible, because it violates the no-cloning theorem. Note that what you want to do is not the standard way to do quantum error correction, because you have $n-1$ copies of a state, not an encoded state. If you have some more knowledge about the state, you might want to look into stuff like magic state distillation, e.g. ...

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The circuit in the diagram is for fault-tolerantly measuring the error syndrome of the logical qubit $|\psi_L\rangle$. I.e., $|\psi_L\rangle$ is the logical qubit (a qubit encoded into 7 qubits using the Steane code) whose errors you want to correct. So removing it wouldn't make sense.

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