Notes on nonlinear quantum algorithms
| dc.creator | Czachor, Marek | |
| dc.date | 1998-02-19 | |
| dc.date | 1998-02-23 | |
| dc.date.accessioned | 2026-07-07T06:14:48Z | |
| dc.date.available | 2026-07-07T06:14:48Z | |
| dc.description | Recenty Abrams and Lloyd have proposed a fast algorithm that is based on a nonlinear evolution of a state of a quantum computer. They have explicitly used the fact that nonlinear evolutions in Hilbert spaces do not conserve scalar products of states, and applied a description of separated systems taken from Weinberg's nonlinear quantum mechanics. On the other hand it is known that violation of orthogonality combined with the Weinberg-type description generates unphysical, arbitrarily fast influences between noninteracting systems. It was not therefore clear whether the algorithm is fast because arbitrarily fast unphysical effects are involved. In these notes I show that this is not the case. I analyze both algorithms proposed by Abrams and Lloyd on concrete, simple models of nonlinear evolution. The description I choose is known to be free of the unphysical influences (therefore it is not the Weinberg one). I show, in particular, that the correct local formalism allows even to simplify the algorithm. | |
| dc.description | one 1/4 changed to 1/2, conclusions unchanged | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9802051 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9802051 | |
| dc.identifier | Acta Phys.Slov. 48 (1998) 157 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/93603 | |
| dc.subject | Quantum Physics | |
| dc.title | Notes on nonlinear quantum algorithms | |
| dc.type | text |