maverick280857
- 1,774
- 5
Hi,
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 the quantum Fourier 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!
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 the quantum Fourier 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!