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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.
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)
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')
