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Looking at the list of the intrinsic gates available in Q#, and keeping in mind that we need a gate with the first column being $\begin{bmatrix} \alpha \\ \beta \end{bmatrix}$, you can notice that the gate with all real coefficients is the Ry gate. Now you need to find $\theta$ such that $\cos\frac{\theta}{2}=\alpha$ and $\sin\frac{\theta}{2}=\beta$. We can ...

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First, note that the input (in vector form) will be $\begin{bmatrix} 1 \\ 0 \end{bmatrix}$. And you want the output to be $\begin{bmatrix} \alpha \\ \beta \end{bmatrix}$. Therefore, the matrix that represents the gate you want needs to have the vector you want as output on the first column. To see what the second column needs to be, let’s look at the general ...

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I think you should take all these things into account: How to create a circuit and measurement in both QDK and Qiskit? How to apply quantum algorithm in both QDK and Qiskit? What are the backends that can be linked to by QDK and Qiskit? Special features between those two (Qiskit pulse, Azure quantum, ...) Performance between these two Any restrictions?

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