I'm studying quantum computing right now and trying to implement variational quantum linear solver to solve a system of linear equations. From what I have understood from the paper written by Carlos Bravo Prieto, I can't find the exact solution vector x but a vector that is proportional to the target answer. From here, I am trying to infer the actual solution by taking a square root of my measurement result and multiplying the normalization factor to my measurement result. However, in this process I lose the signs of the the elements in the solution vector. Is there any way or suggestion on how to determine the signs of the elements in the solution vector?



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