Hi,(adsbygoogle = window.adsbygoogle || []).push({});

This is probably trivial, but I don't see it and would therefore appreciate receving inputs.

Suppose we define a state

[tex]|\phi_{lr}\rangle = \sum_{n=0}^{N/r - 1}\sqrt{\frac{r}{N}}|l + n r\rangle[/tex]

How is thequantumFourier transform of this state equal to

[tex]|\tilde{\phi}_{lr}\rangle = \sum_{m=0}^{r-1}\alpha_{m}\left|\frac{m N}{r}\right\rangle[/tex]

where [itex]|\alpha| = \sqrt{1/r}[/itex] for all [itex]m[/itex]?

This is from http://www-bcf.usc.edu/~tbrun/Course/lecture13.pdf.

Thanks in advance!

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# Quantum Fourier Transform of Periodic States

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