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I'm looking for a quantum circuit that permits generating a uniform superposition of all possible permutations for example if we have as input $|0123\rangle$ the output will be the uniform superposition of all possible permutation $1/a(|0123\rangle+|1023\rangle+|0213\rangle+.....+|3210\rangle)$. I have already implemented a circuit with SWAP gates but the problem is I'm not getting the uniform superposition.

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    $\begingroup$ seems related to quantumcomputing.stackexchange.com/q/11682/55 $\endgroup$
    – glS
    Apr 27, 2022 at 9:15
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    $\begingroup$ It would be helpful if you include the circuit you implemented and the result you get from it. $\endgroup$
    – epelaez
    Apr 27, 2022 at 9:48

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