  We describe a new method for the decomposition of an arbitrary $n$ qubit
operator with entries in $\mathbb{Z}[i,\frac{1}{\sqrt{2}}]$, i.e., of the form
$(a+b\sqrt{2}+i(c+d\sqrt{2}))/{\sqrt{2}^{k}}$, into Clifford+$T$ operators
where $n\le 2$. This method achieves a bound of $O(k)$ gates using at most one
ancilla using decomposition into $1$- and $2$-level matrices which was first
proposed by Giles and Selinger.
