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I have always heard that transversality is a sufficient, not a necessary condition for fault-tolerance in quantum computation. However, I have never seen any examples of non-transversal fault tolerant gates. Does anyone know of any?

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    $\begingroup$ There are lots of examples of non-transversal fault-tolerant gates. None of them are simple, unfortunately. To get an idea of what they look like, and find some references, you could look at sections 4.5 and 4.6 of Dan Gottesman's survey article,. $\endgroup$ – Peter Shor Jun 29 '14 at 13:33

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