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The result of the HHL-algorithm is the (amplitude-encoded) solution vector $|x\rangle$.

I was wondering, which useful information could be extracted from this solution without loosing the algorithms speedup by sampling it $O(N)$ times.

What I found is:

However, if I understand the answer to this question correctly, it should also not be possible to find the largest values efficiently.

Can you give more examples ? (Specifically I am interested in a method to efficiently determine if there are components $x_i$ of $x$ that exceed a certain limit)

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