On an implementation of the Solovay-Kitaev algorithm
| dc.creator | Nagy, Attila B. | |
| dc.date | 2006-06-08 | |
| dc.date.accessioned | 2026-07-07T07:19:01Z | |
| dc.date.available | 2026-07-07T07:19:01Z | |
| dc.description | 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 $polylog(1/ε)$ with product length $polylog(1/ε)$, 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. | |
| dc.description | 10 pages, published on the 10th Rhine Workshop on Computer Algebra | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0606077 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0606077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114509 | |
| dc.subject | Quantum Physics | |
| dc.title | On an implementation of the Solovay-Kitaev algorithm | |
| dc.type | text |