Quantum computation from a quantum logical perspective
| dc.creator | Bub, Jeffrey | |
| dc.date | 2006-05-29 | |
| dc.date | 2006-10-28 | |
| dc.date.accessioned | 2026-07-07T07:15:26Z | |
| dc.date.available | 2026-07-07T07:15:26Z | |
| dc.description | It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the information-processing in the three algorithms are presented from a different perspective, in terms of the way in which the algorithms exploit the non-Boolean quantum logic represented by the projective geometry of Hilbert space. From this quantum logical perspective, the XOR algorithm appears directly as a special case of Simon's algorithm, and all three algorithms can be seen as exploiting the non-Boolean logic represented by the subspace structure of Hilbert space in a similar way. Essentially, a global property of a function (such as a period, or a disjunctive property) is encoded as a subspace in Hilbert space representing a quantum proposition, which can then be efficiently distinguished from alternative propositions, corresponding to alternative global properties, by a measurement (or sequence of measurements) that identifies the target proposition as the proposition represented by the subspace containing the final state produced by the algorithm. | |
| dc.description | 17 pages, no figures. The title has been changed, misprints and minor errors have been corrected, and some clarifying remarks have been added | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0605243 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0605243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113257 | |
| dc.subject | Quantum Physics | |
| dc.title | Quantum computation from a quantum logical perspective | |
| dc.type | text |