I am studying the Quantum Fourier Transform and completing some exercises.

I want to write the circuit for the 4-bit Quantum Fourier Transform in terms of specific gates: H, controlled-V, and C-NOT, where H is the Hadamard gate and $V=\mathrm{diag}(1,e^{\pi i/8})$.

So basically I need to rewrite the H and $R_k$ gates in terms of these. Is there s a relation between phase-changing gates that I am missing?



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