{
  "annotation_id": "d3d52530-b78f-4d5b-bc25-4f62cac2729a",
  "date_created": "2026-03-02T18:02:37.041000Z",
  "date_modified": "2026-03-02T18:02:37.041000Z",
  "file_hash": "0082d99e5d2dab0fdad928856f639e7e8a981cfdfc08d4f35dfb5d6b21228bf7",
  "private": false,
  "record": {
    "abstract": "Quantum computers require quantum arithmetic. We provide an explicit\nconstruction of quantum networks effecting basic arithmetic operations: from\naddition to modular exponentiation. Quantum modular exponentiation seems to be\nthe most difficult (time and space consuming) part of Shor\u0027s quantum\nfactorising algorithm. We show that the auxiliary memory required to perform\nthis operation in a reversible way grows linearly with the size of the number\nto be factorised.",
    "arxiv_id": "quant-ph/9511018",
    "authors": [
      "V. Vedral",
      "A. Barenco",
      "A. Ekert"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.54.147",
    "title": "Quantum Networks for Elementary Arithmetic Operations",
    "url": "https://arxiv.org/abs/quant-ph/9511018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3f4d2867-c998-4c3b-b6b1-f427999f1187",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}