A central question in Quantum Computing is how matrices in SU(2) can be
approximated by products over a small set of "generators". A topology will be
defined on SU(2) so as to introduce the notion of a covering exponent
\cite{letter}, which compares the length of products required to covering
SU(2) with ε balls against the Haar measure of ε
balls. An efficient universal set over PSU(2) will be constructed using the
Pauli matrices, using the metric of the covering exponent. Then, the
relationship between SU(2) and S3 will be manipulated to correlate angles
between points on S3 and give a conjecture on the maximum of angles between
points on a lattice. It will be shown how this conjecture can be used to
compute the covering exponent, and how it can be generalized to universal sets
in SU(2).Comment: This is an updated version of arxiv.org:1506.0578