I'm reading the [paper describing the numerical example HHL][1]. The first question related to the Hermitioan-unitary matrix transformation. We can use numpy.linalg.expm to convert Hermitian to unitary matrix - what I did and achieved the result that contradicts to one in paper:

$\begin{pmatrix} 0.51056242-0.79515385j & 0.27532484+0.17678405j \\ 0.27532484+0.17678405j & 0.51056242-0.79515385j \end{pmatrix}$

So, using this matrix, the further result also differs. What did I do wrong?

The second question is related to the result ration of the output vector $\vec{x}$. What the authors write about $\vec{x}$ is that

ratio of $|x_0|^2$ to $|x_1|^2$ is $1:9$.

however the output results show the different ratio: $0.142^2 : 0.361^2 = 1 : 2.54$

The question is resonable: what does the measured ration mean and how tomake outcome to be more "true"?