Don't mind me If I don't expand too much.

The usefulness is due to other gates such as the haddamard gate and unitary operators.

In the case of shor's algorithm, it brings back the complexity from exponential to polynomial (O(n^2log(n))), making large prime factorization much faster but not costless.

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Okay, if that is true the probability has to collapse to 1. My point is you can approach the probability of 1 but it never is absolute. This is the fundamental problem (yes even using those quantum gates) with a quantum array or "vector" the inability to use the information even if you can approach a closer probability.

A high enough probability is always good enough.