CRk gate

The CRk gate is a parametrized controlled phase shift with angle $\theta = \frac{\pi }{2^{k}}$ (radians), defined by:

$\ CR_k = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{\frac{2 \pi i}{2^k}} \end{pmatrix}$

See also the CR gate.

The CRk gate is especially useful for calculating the Quantum Fourier Transform.