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Aug 2, 2017 at 19:57 comment added Craig Gidney @SamJaques Right. I gave one reason that you can't do it but there are also others reasons.
Aug 2, 2017 at 19:05 comment added Sam Jaques So if I had NOT gates that argument wouldn't hold as I could change the the hamming weight with the NOT gate. But the linked paper also says that Fredkin plus NOT still can't generate the Toffoli gate.
Aug 2, 2017 at 19:04 vote accept Sam Jaques
Aug 2, 2017 at 18:57 vote accept Sam Jaques
Aug 2, 2017 at 18:58
Aug 2, 2017 at 17:18 history answered Craig Gidney CC BY-SA 3.0