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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.

Matrix for IQFT

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Read the circuit for the QFT on 2 qubits and reverse and dagger everything

$$ (1 \otimes H)(Controlled(2,S_1^\dagger))(H \otimes 1) $$

Edit:

For how: Implementation of inverse QFT?

This decomposition is $m=2$ on https://en.wikipedia.org/wiki/Quantum_Fourier_transform Note that $R_2 = S$

$1 \otimes H$ to denote Hadamard on the second qubit. $H \otimes 1$ for Hadamard on the first. $Controlled(2,S_1^\dagger)$ for use qubit 2 as the control and assuming that apply $S^\dagger$ on the first qubit.

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  • $\begingroup$ I am not sure I understand the notation. By (1⊗H), do you mean applying a Hadamard gate to the first qubit? And I am not sure what (Controlled(2,S1)) means? Also, could you explain how you came up with this? Thank you in advance. $\endgroup$ – Rahaf Jul 12 at 20:03
  • $\begingroup$ This might help you youtu.be/uuBgK44JrnA $\endgroup$ – Aman Jul 15 at 7:08
  • $\begingroup$ Thank you! I have one last question, how can I represent the controlled-S† gate? I can only find a single-qubit S† gate. $\endgroup$ – Rahaf Jul 15 at 16:18
  • $\begingroup$ if you're implementing using QISKit the video shows the code also. $\endgroup$ – Aman Jul 16 at 8:05

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