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For questions about the set of quantum gates that form a set of gates from which another gate can be produced; this set is analogous the classical set of universal gates (either a NOR gate or a NAND gate can produce any other gate). This tag, however, is not to be used for the classical set of universal gates; those questions are probably more appropriate on Computer Science SE.
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How can a finite set of gates be universal?
$\{H,CCZ\}$ is just the generating set. The set of gates it generates, i.e. $\langle H, CCZ \rangle$, has an infinite number of gates so it could be universal. The argument in Eastin-Knill says the e …