Rotation of a Photon Polarisation with a Unitary

An equal superposition of a qubit (zero is for example horizontal polarization, one is vertical polarization) can be writen as $$ |qrangle = frac{1}{sqrt{2}}(|0rangle pm |1rangle). $$ This state can be produced by so-called Hadamard gate described by matrix $$ H = frac{1}{sqrt{2}} begin{pmatrix} 1 & 1 1 & -1 end{pmatrix}. $$ Application of $H$ on $|0rangle$ leads to superposition $|qrangle = frac{1}{sqrt{2}}(|0rangle + |1rangle)$, application $H$ on $|1rangle$ leads to $|qrangle = frac{1}{sqrt{2}}(|0rangle - |1rangle)$.

Hadamard gate can be decomposed as $H = frac{1}{sqrt{2}}(X+Z)$

where

$$ X = begin{pmatrix} 0 & 1 1 & 0 end{pmatrix} $$

and

$$ Z = begin{pmatrix} 1 & 0 0 & -1 end{pmatrix} $$

So, yes the unitary preparing equal superposition can be composed of two other unitaries. But I would rather call this linear combination than superposition.