The difference between what you have and what is in the paper is that you are calculating the matrix $U = e^{iA}$, and in the paper they calculate: $ U = e^{iAt},$ with $t=3\pi/4$.

The reason they do this is because they already know what the solution is going to be, so they are basically rescaling the matrix $A$ to given them "nicer" eigenvalues that allow them to cheat in the implementation of the eigenvalue inversion step.

As for why your solution is not giving the 1:9 ratio, it could be that if you are using the same angles as used in the paper for the eigenvalue inversion step but your matrix $U = e^{iA}$, then your result is obviously going to be incorrect because you haven't accounted for the $3\pi/4$ scaling for the angles.

The difference between what you have and what is in the paper is that you are calculating the matrix $U = e^{iA}$, and in the paper they calculate: $ U = e^{iAt},$ with $t=3\pi/4$.

The reason they do this is because they already know what the solution is going to be, so they are basically rescaling the matrix $A$ to given them "nicer" eigenvalues that allow them to cheat in the implementation of the eigenvalue inversion step.

As for why your solution is not giving the 1:9 ratio, it could be that if you are using the same angles as used in the paper for the eigenvalue inversion step but your matrix is $U = e^{iA}$, then your result is obviously going to be incorrect because you haven't accounted for the $3\pi/4$ scaling for the angles.