  We propose a method of compiling that permits to identify quantum circuits
able to simulate arbitrary $n$-qubit unitary operations via the adjustment of
angles in single-qubit gates therein. The method of compiling itself extends
older quantum control techniques and stays computationally tractable for
several qubits. As an application we identify compiling universal circuits for
$3$, $4$ and $5$ qubits consisting of $16$, $64$ and $ 256$ CNOTs respectively.
