Design a circuit implementing the unitary matrix

Question

Is it possible to design a circuit implementing the unitary matrix

$$U-begin{bmatrix}
R_{Theta_1} & 0 & 0 & 0 
0 & R_{Theta_2} & 0 & 0 
0 & 0 & R_{Theta_3} & 0 
0 & 0 & 0 & R_{Theta_4} 
end{bmatrix}$$
for given four angles $Theta_1,...,Theta_4$ , where 0 is 2×2-dimensional zero matrix and $R_{Theta}$ is the rotation matrix with angle $Theta$?
If so, can we implement it on the available quantum programming platforms such as Qiskit, CirQ, PyQuil, or ProjectQ?

DaftWullie · Answer

At worst, you could perform the construction

but depending on your different rotations, you may be able to make some efficiency savings. For example, one improvement that you can always make is you could start by applying $R_1$ on the first qubit without controlling it off anything, and then applying $R_iR_1^dagger$ for the other three controlled-controlled operations.

Design a circuit implementing the unitary matrix

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