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Is there a way to implement a projector gate in a middle of a circuit?. For instance, assuming I have a Bell state $|00\rangle+|11\rangle$, I'd like to apply a projector on the first qubit onto state $|1\rangle$ (operator $|1\rangle\langle 1|$). Meaning that I will be left with $|1\rangle|1\rangle$.Is it possible to do such thing in the middle, and then apply the rest circuit? Also, is there a way to apply a general nonunitary gate without performing real measurements or qasm, only statevector.

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