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I want to create a two-qubit quantum circuit for a function with these inputs and outputs:

f(00)=10

f(01)=10

f(10)=01

f(11)=01

I do not know how to think about this problem systematically and come up with a quantum circuit. Please note that I am using Qiskit so consider the Qiskit order.

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  • $\begingroup$ Thanks for the comment @MarcoFellous-Asiani. It is going to be an oracle for Simon's Algorithm. Does it make a difference? $\endgroup$
    – Hamideh
    May 10, 2023 at 10:27

1 Answer 1

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In Simon's algorithm, the oracle maps $|0\rangle|x\rangle$ to $|f(x)\rangle|x\rangle$. In your case: $$|00\rangle|00\rangle \rightarrow |10\rangle|00\rangle$$ $$|00\rangle|01\rangle \rightarrow |10\rangle|01\rangle$$ $$|00\rangle|10\rangle \rightarrow |01\rangle|10\rangle$$ $$|00\rangle|11\rangle \rightarrow |01\rangle|11\rangle$$

Note: Like Qiskit, I'm using little-endian bit ordering.

This is a unitary operation and can be easily implemented:

circ = QuantumCircuit(4)

circ.cx(1, 2)
circ.cx(2, 3)
circ.x(3)

enter image description here

And to test the output of this circuit, you can use this code snippet:

from qiskit.quantum_info import Statevector

sv = Statevector.from_label('00++').evolve(circ)
sv.draw('latex')
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  • $\begingroup$ It is going to be an oracle for Simon's Algorithm. Does it make a difference? $\endgroup$
    – Hamideh
    May 10, 2023 at 10:26
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    $\begingroup$ Yes! I updated my answer accordingly. $\endgroup$ May 10, 2023 at 16:53
  • $\begingroup$ Thanks. It seems to be correct. How did you come up with such a circuit? I am trying to develop my intuition about quantum circuits. $\endgroup$
    – Hamideh
    May 12, 2023 at 8:13

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