質問: \ sum_n e ^ {2 \ pi in} | x_n \を準備できるかどうかまだわかりません。たとえば、rangle \ langle x_n | $ 。 ベクトル $ | x_n \ rangle $ を順序付けることに興味はありません。簡単にインデックスを付ける方法があるかどうかだけです。この問題が以前に文学で取り上げられたかどうかはわかりませんし、どこを見ればよいのかもわかりません。誰かがいくつかの洞察を持っていたらうれしいです。
回答: The root of the issue here is how do you map between the values $\theta_n$ and $n$. *A priori* there is no way of doing this because the values $n$ are a completely abstract labelling. It wouldn't make any difference if I rearranged all the labels $n$. So, you have defined the $n$s to be a particular order that you want. Presumably as part of that, you know how to identify, given a $\theta_n$, what the value of $n$ is. Whatever mental process that you go through to identify it, you need to translate that into a circuit which you would apply on the ancilla register. Incidentally, are the coefficients $x_{in}$ known? If so, you should be able to construct a transformation directly rather than having to use phase estimation.