# 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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### Clarification about QTF proof regarding equality of QFT application and circuit application

I'm self learning quantum computing through IBM's Qiskit's learning section (which I really like), and I've stumbled across an inequality that I don't quite understand fully. This must be really easy, ...
1 vote
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### DFT like operation in the third step of Period finding and Discrete Logarithm algorithm

In the third step of the algorithm for discrete logarithm, the state $$|\hat{f}(l_1,l_2)\rangle=\frac{1}{\sqrt{r}}\sum_{j=0}^{r-1}e^{-2\pi il_2j/r}|{f}(0,j)\rangle$$ is introduced which is stated to ...
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### How to intuitively interpret the QFT of a state?

According to wikipedia, In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. Given the ...
• 245
1 vote
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### Is Quantum Fourier Transform defined for the standard basis only?

I'm reading the definition on Wikipedia for QFT which is identical to the definition of my professor and they define: $$|x\rangle = \sum_{i=0}^{N-1} x_i |i\rangle$$ And then the QFT of $|x\rangle$ is:...
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### Why do we need to reverse the order of qubits in Quantum Fourier Transform? [duplicate]

Looking at Qiskit's QFT tutorial, their implementation of QFT requires you to swap the qubits at the end (Nielsen and Chuang do this too). I'm wondering why this is the case. Can we flip the gates ...
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