Talk:Quantum Fourier transform

This page is to me lacking an explanation of how the quantum fourier transform is in practice built up out of a combination of Hadamard and controlled rotation gates, a good explanation can be found at sbandrews 18:37, 18 December 2006 (UTC)

I agree that the page lacks information about the quantum circuit implementation of the QFT. Also, it seems to me that the definition of the QFT given here is backwards to the usual definition of a Fourier transform. That is, the definition here looks like it is actually for the inverse QFT. To see what I mean, compare this article with the Discrete Fourier Transform, or with just the Fourier Transform articles. It makes sense to me that the FT should have a minus sign. The whole point of the FT is to extract a frequency spectrum. However, this is further confused by the fact that the definition given here matches the definition in Nielsen & Chuang's book. Karadoc** 04:08, 2 July 2007 (UTC)

I noticed that too about the minus sign, here and in other QFT papers, perhaps it is just a covention amongst QFT researchers, as it will (i think) still give a fourier transform, just with the coefficients reflected about k=0, if it *is* a convention it would be worth referring to it in the article sbandrews (t) 05:37, 2 July 2007 (UTC)

What happened to the old circuit diagram? The recursive implementation of QFT is so much nicer. And whose idea was it to include screen-grabs of messing around in q-kit. Call me a conspiracist, but methinks someone might be trying to promote q-kit via wikipedia. — Preceding unsigned comment added by 134.160.214.34 (talk) 05:06, 15 June 2018 (UTC)

Advertisement

An account called Dev.qkit has added three references in the article to their website, along with some terrible low resolution gifs of their product. I have removed them. They are not even constructive to the article. I hope they do not come back. — Preceding unsigned comment added by 2610:148:1F02:7000:72BF:18D6:948:D41B (talk) 02:27, 7 October 2019 (UTC)

Circuit

Shouldn't the second wire have the transformations $H,R_{2},R_{3},...R_{n-1}$? The diagram makes it seems like it doesn't continue after $R_{2}$. --132.69.202.250 (talk) 17:58, 7 February 2020 (UTC)

Inverse QFT

Is the matrix for the Inverse QFT the same as the "forward" QFT, just with negative exponents? Just asking for clarification if I interpreted the notation correctly - I find the matrix form easier to read than the summation formula. Abinmorth (talk) 02:38, 5 October 2021 (UTC)

More footnotes

As further improvements are made, please attach inline references to help the reader figure out what content is cited to which source. Thank you. Jehochman ^Talk 11:04, 19 October 2022 (UTC)

Numer of amplitudes in the discrete Fourier transform

It is not clear to me why the number of amplitudes is $2^{n}$, for a general DFT the number of operations required is only $n^{2}$. UrielSeptim (talk) 07:38, 11 April 2023 (UTC)

Some problems

1. In the definition of the Fourier transform I wouldn't use n for the index in the \Sigma, as n is already denoting the number of bits.

1. There is an error in the definition of the R_n gates: the definition does not depend on n. I believe the correct definition should have R_n(2,2) = e^2\pi*i / 2^n
2. Also, again, I wouldn't use n for the indexing of the R_n's.

Doobiefletzet (talk) 13:37, 30 May 2023 (UTC)

Also, i should not stand, as index, because it is the imaginary unit, which is important in these formulas. I rewrited the formulas such that neither i, nor n is used, as index. Gezameszena (talk) 15:32, 19 October 2024 (UTC)

The notation in the section "Over a finite field" for finite field appears to switch from $F_{q}$ to $GF(q)$, which does not seem like it is used anywhere else on the page. It would be good to stick to one convention, probably $\mathbb {F} _{q}$ which is quite commonly used in the literature. Tssal (talk) 02:29, 12 April 2025 (UTC)

Language strangely off

I noticed the language constructs (at least in the definitions paragraph) to be grammatically off consistently, sometimes exceeding the point of clear reference.

For example, the initial sentence of the definition paragraph, as is, states that:

"QFT is classical DFT applied to the vector of amplitudes of a quantum state, which has length N=2^n if it is applied to a register of n qubits."

Besides this being a poor way of introducing a central definition (as opposed to opening with the involved variables types and "roles" in a bit more formal language, followed by the formula itself and than appended with reductions and interpretations), it is also slightly going off the rails eventually: It suggests that the quantum state has length N=2^n if *it* (the state itself?) is aplied to a register of n qubits... which makes no sence and can be resolved to the actual intention only, given one has already understood the involved concepts. This vagueness and strangely specific reference continues through the paragraph.

Also, notions are overextended lingually. for exampme, a "quantum state", has no "vektor of amplitudes", as stated. It has a formal representation (wave function), that one can take the norm of, to get a vektor of amplitudes

As the topic is quite confusing to dive into, those things significantly hinder accessibility. Also, the paragraph just doesnt feel like a sufficiently strict and reviewed source, because it is written so casually. ~2026-50117-18 (talk) 21:26, 15 September 2026 (UTC)