{
  "annotation_id": "5e03519d-5d47-4526-95e9-0193a5298c7e",
  "date_created": "2026-03-02T18:01:39.216000Z",
  "date_modified": "2026-03-02T18:01:39.216000Z",
  "file_hash": "232340d043046fd51f21183ece4eaf154bfb598d4060b3754c3f1c745c6e93aa",
  "private": false,
  "record": {
    "abstract": "The representation of numbers by tensor product states of composite quantum\nsystems is examined. Consideration is limited to k-ary representations of\nlength L and arithmetic modulo k^{L}. An abstract representation on an L fold\ntensor product Hilbert space H^{arith} of number states and operators for the\nbasic arithmetic operations is described. Unitary maps onto a physical\nparameter based tensor product space H^{phy} are defined and the relations\nbetween these two spaces and the dependence of algorithm dynamics on the\nunitary maps is discussed. The important condition of efficient implementation\nby physically realizable Hamiltonians of the basic arithmetic operations is\nalso discussed.",
    "arxiv_id": "quant-ph/0009124",
    "authors": [
      "Paul Benioff"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The Representation of Numbers by States in Quantum Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0009124"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9eeef25c-d5fd-45d8-8b3c-0cb3ff3ba290",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}