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

  1. Apr 30, 2015 #1
    I'm currently working through Nielsen & Chuang's section on the circuit design for implementing the QFT. I'm confused as to why swap gates are used in the model to swap the order of qubits. Heres what i'm looking at http://www.johnboccio.com/research/quantum/notes/QC10th.pdf [Broken] page 247 figure 5.1
    Can anybody help?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Apr 30, 2015 #2

    Strilanc

    User Avatar
    Science Advisor

    Here's a blog post about the QFT with some puzzles in a circuit simulator.

    The basic reason is that the QFT's output has the qubits in the reverse order of what you typically want. It switches you from big-endian bits to little-endian bits (or vice versa), so that the amplitude of the state 10010 corresponds to the 7/N frequency instead of the 18/N frequency (or vice-versa).

    You don't have to swap them back into the right order, it just makes it easier to think about the QFT when used as a tool because you're keeping the endian-ness consistent. It makes the result match the usual definition of the discrete Fourier transform, where F(1) corresponds to the lowest non-zero frequency (instead of what F(N-1) corresponds to).
     
    Last edited by a moderator: May 7, 2017
  4. May 1, 2015 #3
    Thats cleared that up, Thanks
     
  5. May 24, 2015 #4
    Do you mean the 9/N frequency not 7/N. Am I right in saying the qubits in your example reversed would read 01001=9?
     
  6. May 24, 2015 #5

    Strilanc

    User Avatar
    Science Advisor

    Yeah, my mistake.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Quantum Fourier Transform
  1. Fourier Transform (Replies: 8)

Loading...