# Tag Info

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### Why can the QFT be replaced by Hadamard gates?

While the QFT and Hadamard transforms are different, their action on the input state $|00\ldots 0\rangle$ is identical; both produce the uniform superposition of all states. So, if you've got a choice ...
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### How do I prove that the Hadamard satisfies $H\equiv e^{i\pi H/2}$?

First of all, note that the statement, as written, is wrong (or rather, it is correct only as long as the "$\equiv$" symbol is taken to mean "equal up to a phase"). An easy way to see it is by ...
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• 59.4k

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

You can easily check that $H^1=XHX$, which is another way to say that $H^1$ is the same as $H$ modulo swapping $|0\rangle$ and $|1\rangle$. This means that it is a different gate. On the other hand, ...
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### Simple algebraic explanation for normalizing states

The coefficient $\frac{1}{\sqrt{2^3}}$ is the normalization factor: if you have a 3-qubit state that is an equal superposition of 8 basis states, its norm still has to be 1; thus the squared amplitude ...
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### $H = e^{i\pi/4} \sqrt{iNOT}$?
It cannot be the case that $H=e^{i\pi/4}\sqrt{iNOT}$. Whatever your interpretation of $iNOT$ (I'd agree with your definition), just square the thing. $H^2=I$, the identity, and so it is certainly not ...