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Find the decomposition of the following matrix into two level unitary matrices:

$$ \frac{1}{2} \begin{pmatrix} 1 & 1 & 1 & 1\\ 1 & i & -1 & -i\\ 1 & -1 & 1 & -1\\ 1 & -i & -1 & i\\ \end{pmatrix} $$

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This is a Quantum Fourier Transform and the Wiki page provides a generic decomposition:

enter image description here

Can you find your two qubit version?

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