For a <finite abelian group> $G$ and its <character group of a finite abelian group> $\widehat G$, the <quantum Fourier transform over a finite abelian group> is
$$
\operatorname{QFT}_G|g\rangle
=\frac1{\sqrt{|G|}}\sum_{\chi\in\widehat G}\chi(g)|\chi\rangle.
$$
Replacing $\chi(g)$ by its complex conjugate gives the equally common inverse-transform convention.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 324 / 4 / a / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-324/4/a/i/solution