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Using Python how can I implement a quantum circuit that returns $|01\rangle$ or $|10\rangle$ using only $CX$, $RX$ and $RY$ gates, starting with random parametric gates as parameters and optimizing it using gradient descent or other optimization algorithm?

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    $\begingroup$ Can you show what you have tried so far to answer this question? $\endgroup$
    – e-eight
    Sep 14 '20 at 18:28
  • $\begingroup$ I have used IBM Quantum Experience and have used an Rx gate (using pi/2 as theta) on qubit 1 $\endgroup$ Sep 24 '20 at 5:35
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One potential combo is $ RY(\theta)$ on qubit 1, $CX$ from qubit 1 to qubit 2, then $RX(\pi)$ on qubit 2. This would be the following transformation:

$$ |0\rangle |0\rangle \mapsto (\cos \frac{\theta}{2} |0\rangle + \sin \frac{\theta}{2}|1\rangle)|0\rangle \mapsto \cos \frac{\theta}{2} |00 \rangle + \sin \frac{\theta}{2} |11\rangle \mapsto \cos \frac{\theta}{2} |01 \rangle + \sin \frac{\theta}{2} |10\rangle $$

This could be implemented in Python with QISKit/Q#/etc.

(Matrices for $RX$, $RY$: https://docs.microsoft.com/en-us/qsharp/api/qsharp/microsoft.quantum.intrinsic.rx / https://docs.microsoft.com/en-us/qsharp/api/qsharp/microsoft.quantum.intrinsic.ry)

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