{
  "annotation_id": "41c15d27-726a-4e2a-9d29-bdd463b3a1f5",
  "date_created": "2026-03-02T18:01:52.563000Z",
  "date_modified": "2026-03-02T18:01:52.563000Z",
  "file_hash": "295af127f97622277c5739b2125fea608a5a5a4099a92ef07c4cfe5cd47b771e",
  "private": false,
  "record": {
    "abstract": "We present an efficient quantum algorithm for estimating Gauss sums over\nfinite fields and finite rings. This is a natural problem as the description of\na Gauss sum can be done without reference to a black box function. With a\nreduction from the discrete logarithm problem to Gauss sum estimation we also\ngive evidence that this problem is hard for classical algorithms. The workings\nof the quantum algorithm rely on the interaction between the additive\ncharacters of the Fourier transform and the multiplicative characters of the\nGauss sum.",
    "arxiv_id": "quant-ph/0207131",
    "authors": [
      "Wim van Dam",
      "Gadiel Seroussi"
    ],
    "categories": [
      "quant-ph",
      "cs.DM",
      "math.NT"
    ],
    "title": "Efficient Quantum Algorithms for Estimating Gauss Sums",
    "url": "https://arxiv.org/abs/quant-ph/0207131"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "32a14afd-f168-4d6d-9451-ef0bb0d5f5c8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}