dorsal/arxiv
View SchemaNotes on nonlinear quantum algorithms
| Authors | Marek Czachor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9802051 |
| URL | https://arxiv.org/abs/quant-ph/9802051 |
| Journal | Acta Phys.Slov. 48 (1998) 157 |
Abstract
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.
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"abstract": "Recenty Abrams and Lloyd have proposed a fast algorithm that is based on a\nnonlinear evolution of a state of a quantum computer. They have explicitly used\nthe fact that nonlinear evolutions in Hilbert spaces do not conserve scalar\nproducts of states, and applied a description of separated systems taken from\nWeinberg\u0027s nonlinear quantum mechanics. On the other hand it is known that\nviolation of orthogonality combined with the Weinberg-type description\ngenerates unphysical, arbitrarily fast influences between noninteracting\nsystems. It was not therefore clear whether the algorithm is fast because\narbitrarily fast unphysical effects are involved. In these notes I show that\nthis is not the case. I analyze both algorithms proposed by Abrams and Lloyd on\nconcrete, simple models of nonlinear evolution. The description I choose is\nknown to be free of the unphysical influences (therefore it is not the Weinberg\none). I show, in particular, that the correct local formalism allows even to\nsimplify the algorithm.",
"arxiv_id": "quant-ph/9802051",
"authors": [
"Marek Czachor"
],
"categories": [
"quant-ph"
],
"journal_ref": "Acta Phys.Slov. 48 (1998) 157",
"title": "Notes on nonlinear quantum algorithms",
"url": "https://arxiv.org/abs/quant-ph/9802051"
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