{
  "annotation_id": "9d89dcad-12a4-4d07-97f3-76a37eac3dcf",
  "date_created": "2026-03-02T18:02:17.088000Z",
  "date_modified": "2026-03-02T18:02:17.088000Z",
  "file_hash": "f9a1e072b5c06a853990d84d2d413ef721508fa6ffc1d3290d6832889a7b3e25",
  "private": false,
  "record": {
    "abstract": "Efficient methods for generating pseudo-randomly distributed unitary\noperators are needed for the practical application of Haar distributed random\noperators in quantum communication and noise estimation protocols. We develop a\ntheoretical framework for analyzing pseudo-random ensembles generated through a\nrandom circuit composition. We prove that the measure over random circuits\nconverges exponentially (with increasing circuit length) to the uniform (Haar)\nmeasure on the unitary group and describe how the rate of convergence may be\ncalculated for specific applications.",
    "arxiv_id": "quant-ph/0503210",
    "authors": [
      "Joseph Emerson",
      "Etera Livine",
      "Seth Lloyd"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.72.060302",
    "journal_ref": "Phys. Rev. A 72, 060302 (2005)",
    "title": "Convergence Conditions for Random Quantum Circuits",
    "url": "https://arxiv.org/abs/quant-ph/0503210"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f7fb98d5-6ff3-4fab-85c8-e8cf8423ca34",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}