The single qubit Hadamard gate is equivalent to 1/sqrt(2) (sigmax + sigmaz)

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### Is quantum superposition state a truth or an assumption?

Please, be patient with my question I already read that there is a heuristic that makes superposition a fact of reality. In addition, this superposition, when observed, it has a state of 0 or 1. ...
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Let's say I have more than one qbits $|0\rangle|1\rangle$ and I want to perform a $H$ on both of them. I know the matrix representation for the Hadamard on a single qbit is $$\frac{1}{\sqrt{2}}\begin{... 3answers 138 views ### How do I prove that the Hadamard satisfies H\equiv e^{i\pi H/2}? How can I demonstrate on the exponential part equality of the Hadamard matrix:$$H=\frac{X+Z}{\sqrt2}\equiv\exp\left(i\frac{\pi}{2}\frac{X+Z}{\sqrt2}\right).$$In general, how can I demonstrate on: \... 2answers 357 views ### Could the Hadamard gate have been constructed differently with similar characteristics? Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it H^1.$$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}H^1 = \begin{bmatrix}-1&1\\1&...
I found this explanation. "The Hadamard gate can also be expressed as a 90º rotation around the Y-axis, followed by a 180º rotation around the X-axis. So $H=XY^{1/2}H = X Y^{1/2}H=XY^{1/2}$." Can ...