Uniform Finite Generation of Compact Lie Groups and universal quantum gates
| dc.creator | D'Alessandro, D. | |
| dc.date | 2001-11-24 | |
| dc.date.accessioned | 2026-07-07T06:03:14Z | |
| dc.date.available | 2026-07-07T06:03:14Z | |
| dc.description | Consider a compact connected Lie group $G$ and the corresponding Lie algebra $\cal L$. Let $\{X_1,...,X_m\}$ be a set of generators for the Lie algebra $\cal L$. We prove that $G$ is uniformly finitely generated by $\{X_1,...,X_m\}$. This means that every element $K \in G$ can be expressed as $K=e^{Xt_1}e^{Xt_2} \cdot \cdot \cdot e^{Xt_l}$, where the indeterminates $X$ are in the set $\{X_1,...,X_m \}$, $t_i \in \RR$, $i=1,...,l$, and the number $l$ is uniformly bounded. This extends a previous result by F. Lowenthal in that we do not require the connected one dimensional Lie subgroups corresponding to the $X_i$, $i=1,...,m$, to be compact. We discuss the consequence of this result to the question of universality of quantum gates in quantum computing. | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0111133 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0111133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/89860 | |
| dc.subject | Quantum Physics | |
| dc.title | Uniform Finite Generation of Compact Lie Groups and universal quantum gates | |
| dc.type | text |