{
  "annotation_id": "4d239ecc-d9de-43fb-bdb1-e110d293c1c6",
  "date_created": "2026-03-02T18:01:49.221000Z",
  "date_modified": "2026-03-02T18:01:49.221000Z",
  "file_hash": "461b8743d0674bb51ddc56d1209d69d4e7202785e68917c5570df7c956e7122b",
  "private": false,
  "record": {
    "abstract": "We give a quantum algorithm for solving a shifted multiplicative character\nproblem over Z/nZ and finite fields. We show that the algorithm can be\ninterpreted as a matrix factorization or as solving a deconvolution problem and\ngive sufficient conditions for a shift problem to be solved efficiently by our\nalgorithm. We also show that combining the shift problem with the hidden\nsubgroup problem results in a hidden coset problem. This naturally captures the\nredundancy in the shift due to the periodic structure of multiplicative\ncharacters over Z/nZ.",
    "arxiv_id": "quant-ph/0205034",
    "authors": [
      "Lawrence Ip"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Solving Shift Problems and Hidden Coset Problem Using the Fourier   Transform",
    "url": "https://arxiv.org/abs/quant-ph/0205034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4219ea3f-1e91-4982-a52f-15ac651d3377",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}