Quantum algorithms for solvable groups
| dc.creator | Watrous, John | |
| dc.date | 2000-11-07 | |
| dc.date | 2001-01-26 | |
| dc.date.accessioned | 2026-07-07T06:01:07Z | |
| dc.date.available | 2026-07-07T06:01:07Z | |
| dc.description | In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of a subgroup in a given solvable group, reduce to computing orders of solvable groups and therefore admit polynomial-time quantum algorithms as well. Our algorithm works in the setting of black-box groups, wherein none of these problems can be computed classically in polynomial time. As an important byproduct, our algorithm is able to produce a pure quantum state that is uniform over the elements in any chosen subgroup of a solvable group, which yields a natural way to apply existing quantum algorithms to factor groups of solvable groups. | |
| dc.description | 13 pages. Several corrections | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0011023 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0011023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/89164 | |
| dc.subject | Quantum Physics | |
| dc.title | Quantum algorithms for solvable groups | |
| dc.type | text |