{
  "annotation_id": "d33c9642-cad4-43ed-a959-5e73a6482c9a",
  "date_created": "2026-03-02T18:01:56.516000Z",
  "date_modified": "2026-03-02T18:01:56.516000Z",
  "file_hash": "c999f5cc3dc9a27ab18be17fc87b1832f83d22790bb4c4502ed0164c4fb9623b",
  "private": false,
  "record": {
    "abstract": "In this paper, we use the methods found in quant-ph/0201095 to create a\ncontinuous variable analogue of Shor\u0027s quantum factoring algorithm. By this we\nmean a quantum hidden subgroup algorithm that finds the period P of a function\nF:R--\u003eR from the reals R to the reals R, where F belongs to a very general\nclass of functions, called the class of admissible functions.\n  One objective in creating this continuous variable quantum algorithm was to\nmake the structure of Shor\u0027s factoring algorithm more mathematically\ntransparent, and thereby give some insight into the inner workings of Shor\u0027s\noriginal algorithm. This continuous quantum algorithm also gives some insight\ninto the inner workings of Hallgren\u0027s Pell\u0027s equation algorithm. Two key\nquestions remain unanswered. Is this quantum algorithm more efficient than its\nclassical continuous variable counterpart? Is this quantum algorithm or some\napproximation of it implementable?",
    "arxiv_id": "quant-ph/0210141",
    "authors": [
      "Samuel J. Lomonaco, Jr.",
      "Louis H. Kauffman"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "A Continuous Variable Shor Algorithm",
    "url": "https://arxiv.org/abs/quant-ph/0210141"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eb96fe9a-1ec3-465d-bd85-7af44246a333",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}