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I am starting with Q# and I would like to know how can I get the following qubit state:

0.8|0⟩ + 0.2|1⟩

from a qubit initialized as |0⟩.

Thanks in advance!

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First, a clarification that in order to have a properly-normalized state, you probably intend to create a state something like: $\sqrt{0.8} \left| 0 \right> + \sqrt{0.2} \left| 1 \right>$. Here the probability of measuring $\left| 0 \right>$ is 0.8 and the probability of measuring $\left| 1 \right>$ is 0.2, when measuring in the computational basis.

Now, starting with a qubit in the $\left| 0 \right>$ state, you can just apply an Ry operation with the appropriate angle. You need to choose the angle such that $\cos({\theta}/{2}) = \sqrt{0.8}$. The ArcCos function will help you here.

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  • $\begingroup$ Perfect! Thank you :) $\endgroup$
    – Antonio
    Commented May 31, 2020 at 11:18

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