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Question 1

4votes

0answers

61views

How to construct a block-diagonal embedded Fourier matrix?

We know the quantum circuit representation of Fourier operator. Now, I want the quantum circuit for the following unitary matrix using single and two qubit gates:$$U =\begin{pmatrix}F_3 & 0 \\...

Gourav Sinha

41

askedNov 21 at 13:15

Question 2

2votes

2answers

78views

QFT of two superposed states

Given a N qubits quantum register, in state $1/\sqrt{2}(|a\rangle+|b\rangle)$, my goal is to find sum of a and b (a+b) or subtraction (b-a).Taking classical example, let [7, 13], the discret FT will ...

user12910

501

askedNov 20 at 22:47

Question 3

5votes

1answer

665views

Why QFT-based arithmetic?

In what follows, I am mostly interested in exact arbitrary-precision arithmetic. Quantum arithmetic is an active research topic. Of course any classical algorithm for arithmetic can be expressed as a ...

delete000

233

askedSep 4 at 13:02

Question 4

5votes

0answers

87views

Is the semi-classical QFT tractable when using random angles and multipliers instead of structured ones?

The semi-classical quantum Fourier transform works by repeatedly preparing a control qubit in a state $R_Z(\phi)|+\rangle$ (where $\phi$ is adapted depending on previous measurements), performing $U^m$...

Craig Gidney

50.1k

askedJun 24 at 22:11

Question 5

4votes

0answers

139views

Prepare a superposition with period gcd(A, B) in log depth

According to John Watrous, it's not known how to test coprimality in logarithmic depth. This is a special case of there being no known way to compute an n-bit gcd in less than $\Omega(n / \log n)$ ...

Craig Gidney

50.1k

askedMar 29 at 18:35

Question 6

1vote

1answer

146views

Studying QFT circuit noise in Qiskit comparing statevectors with state_fidelity

I am using Qiskit latest version and I am trying to compare the noise of a QFT circuit. I already managed to do so with circuits like the one for the Bernstein-Vazirani Algorithm, where i get to ...

eddie felson

49

askedFeb 12 at 12:47

Question 7

2votes

1answer

271views

Why does Quantum Phase Estimation first 'naturally' convert the phase into its Fourier basis states?

In QPE, we first accumulate the phase in control bits and then apply inverse QFT to them to get the actual phase.So it means that QPE must be converting the phase into its Fourier basis states in the ...

shrini1000

285

askedJan 12 at 6:18

Question 8

6votes

2answers

763views

How does the QFT circuit correspond to the FFT algorithm?

As mentioned at length in this answer, in good part taking inspiration from these online pdf notes, there is a very direct relation between the quantum Fourier transform (QFT) circuit and the (...

glS♦

27.8k

askedNov 10, 2024 at 16:26

Question 9

8votes

1answer

122views

Exponentiating a product of QFT-related operators

Is there a smart way to implement $e^{i\theta\,\Phi\,\rm{QFT} \, \Phi \, \rm{QFT}^\dagger}$, where both $\Phi \propto\sum_j2^jZ_j$ and $\rm{QFT}$ act on the same set of registers? Even an approximate ...

mavzolej

2,311

askedNov 6, 2024 at 17:25

Question 10

1vote

1answer

156views

Can we find the quantum state using the Bloch vector in the Bloch sphere?

I had a question about qft. When we apply QFT in a circuit, we can display the qubits separately in the bloch sphere with the plot_bloch_multivector function. I realized that the bloch vectors do not ...

Süleyman Emir Yılmaz

31

askedSep 1, 2024 at 9:20

Question 11

6votes

1answer

102views

Why no $Z$'s in the $\operatorname{F} (\sum_{j=0}^{n-1} 2^j Z_j) \operatorname{F}^\dagger$ operator?

An interesting numerical observation is that an operator defined as $\phi=\sum_{j=0}^{n-1} 2^j Z_j$ upon a QFT is rotated into an operator $\pi=\operatorname{F} \phi \operatorname{F}^\dagger$ which ...

mavzolej

2,311

askedAug 27, 2024 at 17:26

Question 12

3votes

2answers

200views

qiskit DraperQFTAdder

my code:...

Lexiang Xue

73

askedJul 22, 2024 at 11:25

Question 13

2votes

1answer

116views

Unitary Transformation for QFT with 2 base states is giving the columns in the wrong order

I'm trying to reproduce in Qiskit the multiplicative form of the QFT for two qubits. It is similar to what is asked in Nielsen's QCQI book in Exercise 5.2 and Box 5.1. To check the results I'm ...

Gustavo Mirapalheta

215

askedJul 14, 2024 at 5:45

Question 14

4votes

1answer

270views

Defining the QFT over finite fields

The DFT is well-developed over $\mathbb{C}$ with fast quantum algorithms.There is a DFT defined classically over $F_q$ which mirrors the complex case when we have an $N^{th}$ root of unity in $F_q$, ...

Jackson Walters

361

askedJun 24, 2024 at 22:08

Question 15

1vote

1answer

198views

quantum multiplier for large numbers

I am working on a project where I need to calculate 3x+1 for numbers 0 to infinity. I have an 8GB RAM laptop and I am using Cirq. For small numbers, I was able to perform the multiplication using the ...

karen

71

askedJun 17, 2024 at 20:08

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Stack Exchange Network

Questions tagged [quantum-fourier-transform]

How to construct a block-diagonal embedded Fourier matrix?

QFT of two superposed states

Why QFT-based arithmetic?

Is the semi-classical QFT tractable when using random angles and multipliers instead of structured ones?

Prepare a superposition with period gcd(A, B) in log depth

Studying QFT circuit noise in Qiskit comparing statevectors with state_fidelity

Why does Quantum Phase Estimation first 'naturally' convert the phase into its Fourier basis states?

How does the QFT circuit correspond to the FFT algorithm?

Exponentiating a product of QFT-related operators

Can we find the quantum state using the Bloch vector in the Bloch sphere?

Why no $Z$'s in the $\operatorname{F} (\sum_{j=0}^{n-1} 2^j Z_j) \operatorname{F}^\dagger$ operator?

qiskit DraperQFTAdder

Unitary Transformation for QFT with 2 base states is giving the columns in the wrong order

Defining the QFT over finite fields

quantum multiplier for large numbers

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