I was trying to build a $cccx$ gate. According to this paper by Berenco et al., it requires a $\sqrt[4]{X}$ gate. Furthermore, I found another paper by Muradian and Frias with this formula:
$$\sqrt A=\frac{1}{\sqrt{2i}}(iI+A).$$
From this I calculated $\sqrt[4]{X}$, $$ \sqrt[4]{X} = \begin{bmatrix}{\frac{2+i}{2}}&{\frac{-i}{2}}\\{\frac{-i}{2}}&{\frac{2+i}{2}}\end{bmatrix} $$
I am not sure about the result at all! I used MATLAB to determine the fourth power of $\sqrt[4]{X}$ matrix, but it doesn't give $X$ matrix. Also, I am confused because there should be four matrices, and I don't know how to implement them in Qiskit either.