# Questions tagged [quantum-fourier-transform]

Quantum Fourier Transform (QFT) is a linear transformation on quantum bits and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem. (Wikipedia)

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### What is this equation for coin operator is trying to do in this quantum walk for Non-regular graph? This coin operator is called Fourier coin

I am reading the following paper: Discrete-time quantum walk on complex networks for community detection by Kanae Mukai We define the Coin operator $C$ by: $C=C_1\otimes C_2....C_n$ , We define coin ...
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### Shor's algorithm: initialization of second register

I am trying to understand Shor's algorithm. I am not quite sure why the initialization, indicated as $|1\rangle$ in the below image at the bottom left is chosen as it is? I understand the modular ...
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### Qiskit Inverse of a quantum fourier transformation

In the photo provided the Quantum Fourier Transform is depicted in Qiskit before the barrier. I don't understand the result of inverse. Conceptually, should the inverse of the QFT be the same ...
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### Quantum Fourier Transform for general cyclic groups

The QFT on the group $\mathbb{Z}_N$ is given by \begin{equation} QFT\,|k\rangle =\frac{1}{\sqrt{N}} \sum_{j=0}^{N-1} e^{2\pi i\,jk/N}|j\rangle\,. \end{equation} The usual circuit implements the QFT ...
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### Abelian Hidden Subgroup Problem for arbitrary cyclic p-Groups

I had asked a question similar to this one here regarding how to handle the HSP for groups whose cyclic decomposition contains factors whose order is not a power of two. I also had some prior ...
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### How to write a classical version of Shor's algorithm

For learning purposes, I would like to write a classical version of Shor's algorithm. From what I have read, what makes this algorithm fast is the quantum FFT, which is used to find the period of the ...
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### Quantum circuit, Fourier Transform/Decomposition?

Broadly speaking, can we say that quantum circuits are like Fourier Transform/Decomposition? We use qbit like waves, tune it with quantum gates, to find answer. https://ars.els-cdn.com/content/image/3-...
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### Constructing arbitrary functions for the Abelian HSP

My question might be similar to Hidden subgroup problem. However, I'm not exactly sure though. In addition, that question doesn't have an answer. I'm trying to create some simple instances of the ...
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### How to obtain the density matrix using tomography in the real device?

I am trying to run the QFT algorithm for n=5 (n number of qubits). The number of experiments that it generates is bigger than the one allowed by the IBM devices (i.e. 75). Therefore, I have tried to ...
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### QFT of 3-bit system

Recently I was learning about QFT(Quantum Fourier Transform). I was learning how QFT is applied with H and cROT gates. I was playing with QFT here. I was testing with 3-Qubit set as you can see in the ...
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### Question Regarding Quantum Period-Finding Fourier Transform Approximation

I am following the 5.4.1 Period-Finding Algorithm in Nielsen and Chuang as shown below: My confusion lies with the second expression of point 3 in the procedure. Why is the second expression an ...
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### How to check if a quantum circuit is deterministic?

I'm trying to find a way to check if a given quantum circuit is essentially a classical one (up to changes in phase). Given a description of a quantum circuit by a list (of size $l$) of ordered ...
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### The control phase gate in Quantum fourier transform and the question it brings up regarding control gates in general

I have a question that's arose from reading "Quantum computing explained" by David McMahon. On page 212 there's an aspect of his description of the quantum Fourier transform which I don't understand . ...
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### Hidden subgroup problem

Let $H$ be a hidden subgroup of $G_1$ that is indistinguishable from subgroup $H^{\prime}$ by quantum Fourier sampling. Now take a larger group $G_2$ such that it contains $G_1$. Now if I do quantum ...
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### How to decompose the Quantum Fourier Inverse matrix into elementary quantum gates?

I am not sure how to find the following matrix (the inverse of Quantum Fourier Transform) in terms of elementary quantum gates? I am using Qiskit to implement it.
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### Using Quantum Fourier Transform in adding two 2-bit numbers

I am trying to use Qiskit to write a code that uses QFT to add 2 numbers. I am referring to this paper: https://iopscience.iop.org/article/10.1088/1742-6596/735/1/012083 I have a few questions: 1) Is ...
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### What is the intuition of using Hadamard gate in quantum fourier transform?

According to this answer by rrtucci, I still cannot catch the spirit of QFT algorithm. So I would like to ask why are we using the Hadamard gate when computing the Fourier Transform? Moreover, what ...
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### Is the quantum Fourier transform efficient if only one control-phase is allowed in the gate set

I have seen Why can the Discrete Fourier Transform be implemented efficiently as a quantum circuit?. This is not a duplicate. I am familiar with the decomposition of the QFT from Nielsen&Chuang ...
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### Quantum Fourier Transform without SWAPs

The Quantum Fourier Transform from Nielsen and Chuang chapter 5 is pictured here: In the textbook the author refers to "swap gates at the end of the circuit which reverse the order of the qubits". ...
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### Why should we use inverse QFT instead of QFT in Shor's algorithm?

Why should we use inverse QFT instead of QFT in Shor's algorithm? When I tried to simulate Shor's algorithm for small numbers, I got an answer even when I used just QFT instead of inverse QFT.
This question is about Lemma $7.1.2$ in Kaye, Laflamme, and Mosca's textbook: Let $\omega = \frac{x}{2^n} = 0.x_1x_2\ldots x_n$ be some fixed number. The phase estimation algorithm applied to the ...