{
  "annotation_id": "d1f05df4-f556-449b-931c-4e1e5246876f",
  "date_created": "2026-03-02T18:01:55.662000Z",
  "date_modified": "2026-03-02T18:01:55.662000Z",
  "file_hash": "bdfab9030f28653ac7e50a1ae0356ddc0822acf04d656ccdbf12e620498909cf",
  "private": false,
  "record": {
    "abstract": "In this paper it has been described how to use the unitary dynamics of\nquantum mechanics to solve the prime factorization problem on a spin ensemble\nwithout any quantum entanglement. The ensemble quantum computation for the\nprime factorization is based on the basic principle that both a closed quantum\nsystem and its ensemble obey the same unitary dynamics of quantum mechanics if\nthere is not any decoherence effect in both the quantum system and its\nensemble. It uses the NMR multiple-quantum measurement techniques to output the\nquantum computational results that are the inphase multiple-quantum spectra of\nthe spin ensemble. It has been shown that the inphase NMR multiple-quantum\nspectral intensities used to search for the period of the modular exponential\nfunction may reduce merely in a polynomial form as the qubit number of the spin\nensemble. The time evolution process of the modular exponential operation on\nthe quantum computer obeys the unitary dynamics of quantum mechanics and hence\nthe computational output is governed by the quantum dynamics. This essential\ndifference between the quantum computer and the classical one could be the key\npoint for the quantum computation outperforming the classical one in the prime\nfactorization on a spin ensemble without any quantum entanglement. It has been\nshown that the prime factorization based on the quantum dynamics on a spin\nensemble is locally efficient at least. This supports the conjecture that the\nquantum dynamics could play an important role for the origin of power of\nquantum computation and quantum entanglement could not be a unique resource to\nachieve power of quantum computation in the prime factorization.",
    "arxiv_id": "quant-ph/0302153",
    "authors": [
      "Xijia Miao"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "A prime factorization based on quantum dynamics on a spin ensemble (I)",
    "url": "https://arxiv.org/abs/quant-ph/0302153"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4c89b76e-cbe4-4b10-9590-52639f8ed58d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}