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I'm confused about the definition of the Clifford hierarchy and would like resources to learn more. For example, in https://arxiv.org/abs/1603.04230, they define the hierarchy as: Campbell and O'Gorman's definition of the hierarchy However, in prior stack exchange posts, it is defined as follows: Stack exchange definition Where membership has been interchanged. Which is correct, and how does it relate to the claim that $R_\ell = \exp (i \pi / 2^\ell Y) \in \mathcal{C}^\ell$? What resources are useful to learn more?

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