  Given an arbitrary $2^w \times 2^w$ unitary matrix $U$, a powerful matrix
decomposition can be applied, leading to four different syntheses of a
$w$-qubit quantum circuit performing the unitary transformation. The
demonstration is based on a recent theorem by F\"uhr and Rzeszotnik,
generalizing the scaling of single-bit unitary gates ($w=1$) to gates with
arbitrary value of~$w$. The synthesized circuit consists of controlled 1-qubit
gates, such as NEGATOR gates and PHASOR gates. Interestingly, the approach
reduces to a known synthesis method for classical logic circuits consisting of
controlled NOT gates, in the case that $U$ is a permutation matrix.
