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For questions about matrix representations of quantum gates.

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Could the Hadamard gate have been constructed differently with similar characteristics?

Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$. $$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$ $$H^1 = \begin{bmatrix}-1&1\\1&1\end{bmatrix}$ …
Nate Lowry's user avatar