{
  "annotation_id": "651ed07c-29dd-46d6-acc2-81389c63f06d",
  "date_created": "2026-03-02T18:01:59.545000Z",
  "date_modified": "2026-03-02T18:01:59.545000Z",
  "file_hash": "c5c3e60fad1773d648078f08b3a013f993e721eb81c234fbfa57ff449f4cae4f",
  "private": false,
  "record": {
    "abstract": "We analyze quantum computers which perform Shor\u0027s factoring algorithm, paying\nattention to asymptotic properties as the number L of qubits is increased.\nUsing numerical simulations and a general theory of the stabilities of\nmany-body quantum states, we show the following: Anomalously fluctuating states\n(AFSs), which have anomalously large fluctuations of additive operators, appear\nin various stages of the computation. For large L, they decohere at anomalously\ngreat rates by weak noises that simulate noises in real systems. Decoherence of\nsome of the AFSs is fatal to the results of the computation, whereas\ndecoherence of some of the other AFSs does not have strong influence on the\nresults of the computation. When such a crucial AFS decoheres, the probability\nof getting the correct computational result is reduced approximately\nproportional to L^2. The reduction thus becomes anomalously large with\nincreasing L, even when the coupling constant to the noise is rather small.\nTherefore, quantum computations should be improved in such a way that all AFSs\nappearing in the algorithms do not decohere at such great rates in the existing\nnoises.",
    "arxiv_id": "quant-ph/0308005",
    "authors": [
      "Akihisa Ukena",
      "Akira Shimizu"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.69.022301",
    "journal_ref": "PRA 69, 022301 (2004)",
    "title": "Appearance and Stability of Anomalously Fluctuating States in Shor\u0027s   Factoring Algorithm",
    "url": "https://arxiv.org/abs/quant-ph/0308005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "197358eb-18a1-47ba-8b33-a8f395ae3c53",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}