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On the Approximation of the Quantum Gates using Lattices. (arXiv:1506.05785v4 [math.QA] UPDATED)
来源于:arXiv
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 $\varepsilon$ balls against the Haar measure of $\varepsilon$
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 $S^3$ will be manipulated to correlate angles
between points on $S^3$ 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 $SU(2)$. 查看全文>>