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Among many paper describing circuit solving period finding problem and discrete logarithm problem (DLP) (for simplity, let's say $g \equiv x^r$ (mod n) and try to find $r$), there are two variants that people usually ignore:

  1. Some paper use inverse QFT instead of QFT.
  2. Before applying QFT, some paper prepare the state as $$\frac{1}{q}\sum_{a, b}|a, b, g^ax^b⟩$$ instead of $$\frac{1}{q}\sum_{a, b}|a, b, g^ax^{-b}⟩$$

From this post and probability reduction we know these variants do not affect the probability analysis. However, in pratical implementation, variant no. 2 may save one quantum modular inverse operation. Also, I heard that using inverse QFT makes the probability analysis neater than using QFT, but I did not find any supporting document.

Therefore, is there any other reason that such preferences are made?

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