# 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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### Hamiltonian of Qiskit QFT is not hermitian

I am trying to generate the Hamiltonian of a quantum Fourier transform by taking the log of the corresponding unitary using qiskit and scipy. I don't find a hermitian matrix. Why? ...
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### Equating the state of the Phase Estimation algorithm to $\frac{1}{2^{t/2}}\sum_{k=0}^{2^t-1} e^{2\pi i\phi k}|k\rangle$

It is stated in the Phase Estimation algorithm in Page 222, Quantum Computation and Quantum Information by Nielsen and Chuang that It seems to say that taking the inverse Quantum Fourier transform of ...
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### Making sense of the terms Polynomial and Exponential Precision in a Quantum Circuit

The quantum circuit construction of the quantum Fourier transform apparently requires gates of exponential precision in the number of qubits used. However, such precision is never required in any ...
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### HHL algorithm explanation in layman terms [duplicate]

Can someone explain what is happening step by step in HHL algorithm in layman terms without maths starting from the first part (quantum phase estimation), than the second part (rotation gate) and ...
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### Formulation of quantum phase estimation in Nielsen and Chuang is different then from other sources?

In a chapter of Quantum Computation and Quantum Information by Nielsen and Chuang (10th edition) about quantum phase estimation I get a little confused. Namely: Before applying inverse QFT our quantum ...
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### Implementation of the Phase Estimation algorithm

I've been working on implementing quantum phase estimation in Qiskit for a $2^n \times 2^n$ Hamiltonian as part of my bachelor project, I'm using Trotterization as my Hamiltonian simulation of choice ...
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### What is the relation between Hadamard transformation and QFT?

I am new to the field and I can't help having a feeling that Hadamard and Fourier Transform are somehow related, but it is not clear to me how. Any explanation on how these two are related would be ...
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### In Shor's algorithm, how is ${\rm QFT}_n|x\rangle$ split into its even and odd components?

I am auditing a course on quantum computing. Since this is not paid, I dont have any staff support to ask questions. Therefore I am asking the stackoverflow community to help me with it. This is ...
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### What are the input and output of QFT and IQFT, respectively?

I have read two opposite explanations about QFT and IQFT from 2 books for beginners of Quantum Computing. Which one is correct? The first book said, if we input an n-qubit non-superposition state into ...
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### What is the quantum query complexity of the period finding routine of Shor's algorithm?

It seems like it should be a function of N - O(log N), to minimise probability of getting a multiple of the period. However, Prof Preskill's lec notes mention: Thus we solve Period Finding if the ...
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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 ...