  In quantum computation we are given a finite set of gates and we have to
perform a desired operation as a product of them. The corresponding
computational problem is approximating an arbitrary unitary as a product in a
topological generating set of $SU(d)$. The problem is known to be solvable in
time $polylog(1/\epsilon)$ with product length $polylog(1/\epsilon)$, where the
implicit constants depend on the given generators. The existing algorithms
solve the problem but they need a very slow and space consuming preparatory
stage. This stage runs in time exponential in $d^2$ and requires memory of size
exponential in $d^2$. In this paper we present methods which make the
implementation of the existing algorithms easier. We present heuristic methods
which make a time-length trade-off in the preparatory step. We decrease the
running time and the used memory to polynomial in $d$ but the length of the
products approximating the desired operations will increase (by a factor which
depends on $d$). We also present a simple method which can be used for
decomposing a unitary into a product of group commutators for $2<d<256$, which
is an important part of the existing algorithm.
