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Sep 5, 2019 at 20:59 comment added glS @Alex personally I would find that a very confusing notation. "Symmetric" is used for matrices such that $A^T=A$. Something like symmetric under exchange of inputs might be better.
Sep 5, 2019 at 20:56 comment added Alex @glS Yep, I meant the last definition that you explained: "they can commute with the SWAP operation". Similar to what DaftWullie said in his comment. So I guess they can be called "symmetric"?
Sep 5, 2019 at 18:26 comment added Mark Spinelli Oh! Sorry, I think you are right - CPhase satisfies your (and the OP's) requirements, but is not bisymmetric as I suggested in another answer.
Sep 5, 2019 at 18:10 comment added glS @MarkS you mean because it satisfies every single one of the conditions, or because I missed that it doesn't satisfy one of them?
Sep 5, 2019 at 17:19 comment added Mark Spinelli The OP's reference to CPhase seems to be a fly in the ointment, no?
Sep 5, 2019 at 16:27 history edited glS CC BY-SA 4.0
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Sep 5, 2019 at 16:12 comment added glS @DaftWullie ah, right, hadn't read that part
Sep 5, 2019 at 16:11 comment added DaftWullie but it is then clarified that the reversal means "exchanging the target qubit with the control qubit"
Sep 5, 2019 at 16:10 comment added glS @DaftWullie why not? "can be reversed and still perform the same operation" reads to me as asking for gates such that $U^{-1}=U^\dagger=U$
Sep 5, 2019 at 15:59 comment added DaftWullie That's what I thought was being asked when I first read the question. I don't think it is though.
Sep 5, 2019 at 15:58 history answered glS CC BY-SA 4.0