Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quantum Fourier Transform of Periodic States

  1. Oct 17, 2011 #1
    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!
     
  2. jcsd
  3. Apr 10, 2012 #2
    I have the same question on it... Any help?
     
  4. Apr 10, 2012 #3
    you must use the Poisson summation formula.
     
  5. Apr 10, 2012 #4
    I have just proved it using similar formulas. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Quantum Fourier Transform of Periodic States
  1. Quantum State (Replies: 28)

  2. Fourier Transform (Replies: 8)

  3. Quantum state (Replies: 24)

  4. Quantum state (Replies: 4)

Loading...