Could someone give an example of this pic?


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This is a picture from Wiki( Can someone give me a simple example by using two qubits?

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Posted 2020-04-12T01:21:55.047

Reputation: 65

1If you apply a unitary $F$ to the first qubit (q[0]), then your state would be the same as if you applied the conjugate transpose $F^\dagger$ to the second qubit (q[1]). Can you be more specific? – Mark S – 2020-04-12T02:05:26.383

could you please edit the title to something that reflects what is being asked? – glS – 2020-04-13T08:01:12.580



Since Fourier transform and inverse Fourier transform for one qubit is only Hadamard gate, for two qubit case following two circuits are equivalent.

First circuit (Fourier transform applied on qubit $q_0$)

Circuit 1

First circuit (inverse Fourier transform applied on qubit $q_1$)

Circuit 2

Both circuits return state

$$ |\psi\rangle = \frac{1}{2}(|00\rangle + |01\rangle + |10\rangle - |11\rangle). $$

EDIT: I have just realized that the gate $F$ is general unitary transformation and not the QFT (I was missleaded by F = Fourier). However, my example is also valid. It is a particular case for two qubits asked for in the question.

Martin Vesely

Posted 2020-04-12T01:21:55.047

Reputation: 7 763