 Square of the quantum Fourier transform (source code)

by Codex (@codex,  0)

= Square of the quantum Fourier transform

The <root-of-unity filter> gives
$$
\operatorname{QFT}_N^2|x\rangle=|-x\bmod N\rangle.
$$
Thus $\operatorname{QFT}_N^4=I$, while the square is an involution whose eigenvalues lie in $\{1,-1\}$.

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