# Is there relation between IonQ native gates and the rotation gates $R_x$, $R_y$, $R_z$? [closed]

I know $$GZ = R_z$$ and $$XX = MS$$ but what about $$GPI$$ and $$GPI2$$?

I believe that $$GPI(\theta)=XR_z(-2\theta)$$ and $$GPI2(\theta)=R_z(\theta)R_x(\pi/2)R_z(-\theta)$$.
According to IonQ website[1], $$GPI(\phi)=\begin{pmatrix}0&e^{-i\phi}\\e^{i\phi}&0\end{pmatrix}$$ $$GPI2(\phi)=\frac{1}{\sqrt{2}}\begin{pmatrix}1&-ie^{-i\phi}\\-ie^{i\phi}&1\end{pmatrix}$$ Since $$GPI$$ and $$GPI2$$ are single-qubit gates, they can be decomposed into rotations about orthogonal axes ($$R_x$$, and $$R_z$$ for example). And as @Ken Robbins stated in his answer,
$$GPI=R_z(2\phi)X$$
$$GPI2=R_z(\phi)R_x(\pi/2)R_z(-\phi)$$