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It's been a long while since I've looked at my thesis, so a lot of my knowledge is pretty rusty, but here goes. If you're looking for the circuit representation of $C_8$, here's the Quirk simulation for it. The first two columns prepare the state $|\phi_0\rangle = \frac{1}{\sqrt{2}}(|001\rangle+|111\rangle)$ in big-endian order (the dominant convention ...


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