{
  "annotation_id": "b9bf0632-2dde-48cf-9ac5-bc416a189a8c",
  "date_created": "2026-03-02T18:02:20.751000Z",
  "date_modified": "2026-03-02T18:02:20.751000Z",
  "file_hash": "0c715b6be7b5edfd5e828e9b7c10027119c1c39b6432dcbd1e9eee2fe089a2fc",
  "private": false,
  "record": {
    "abstract": "The hardness to solve an unstructured quantum search problem by a standard\nquantum search algorithm mainly originates from the low efficiency to amplify\nthe amplitude of the marked state by the oracle unitary operation associated\nwith other known quantum operations. In order to bypass the square speedup\nlimitation of a standard quantum search algorithm it is necessary to develop\nother type of quantum search algorithms. It is described in detail in the paper\nfor a quantum dynamical method to solve the quantum search problems in the\ncyclic group state space. The binary dynamical representation for a quantum\nstate in the Hilbert space of the n-qubit quantum system is generalized to the\nmulti-base dynamical representation for a quantum state in the cyclic group\nstate space. Thus, any quantum state in the cyclic group state space may be\ndescribed completely in terms of a set of dynamical parameters that are closely\nrelated to the symmetric property and structure of the cyclic group. The\nquantum search problem therefore could be solved by determining the set of\ndynamical parameters that describe completely the unknown marked state of the\nsearch problem instead by directly measuring the marked state which is a\nnecessary step in the standard quantum search algorithm. An unstructured\nquantum search problem in the Hilbert space is inevitably affected greatly by\nthe symmetric property and structure of a group. The main attempt of the paper\nis to make use of the symmetric properties and structures of groups to help\nsolving the quantum search problems in the group state spaces. It is shown how\nthe quantum search process could be reduced from the cyclic group state space\nto these cyclic group state subspaces with the help of the symmetric property\nand structure of the cyclic group on a universal quantum computer.",
    "arxiv_id": "quant-ph/0507236",
    "authors": [
      "Xijia Miao"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum search processes in the cyclic group state spaces",
    "url": "https://arxiv.org/abs/quant-ph/0507236"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "78bf617d-604f-4b4d-9280-efe4c053ab9e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}