{
  "annotation_id": "1b44962a-8465-45b6-bd5c-51e397e9fadf",
  "date_created": "2026-03-02T18:02:41.303000Z",
  "date_modified": "2026-03-02T18:02:41.303000Z",
  "file_hash": "565a4779cf740e07676840c878cc2a8ae351241fe58e2353e69fd9febac0a1dd",
  "private": false,
  "record": {
    "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"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ec1f0e6f-d0bd-4aeb-aaa2-a63fec648a14",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}