{
  "annotation_id": "42a5c115-7c18-4360-b5aa-114f281665a2",
  "date_created": "2026-03-02T18:02:03.199000Z",
  "date_modified": "2026-03-02T18:02:03.199000Z",
  "file_hash": "de49e3770300a71d9dfb12b5223cc02254ca6d05bbb2718e49c92780425eb0c9",
  "private": false,
  "record": {
    "abstract": "We study the universality of scaling of entanglement in Shor\u0027s factoring\nalgorithm and in adiabatic quantum algorithms across a quantum phase transition\nfor both the NP-complete Exact Cover problem as well as the Grover\u0027s problem.\nThe analytic result for Shor\u0027s algorithm shows a linear scaling of the entropy\nin terms of the number of qubits, therefore difficulting the possibility of an\nefficient classical simulation protocol. A similar result is obtained\nnumerically for the quantum adiabatic evolution Exact Cover algorithm, which\nalso shows universality of the quantum phase transition the system evolves\nnearby. On the other hand, entanglement in Grover\u0027s adiabatic algorithm remains\na bounded quantity even at the critical point. A classification of scaling of\nentanglement appears as a natural grading of the computational complexity of\nsimulating quantum phase transitions.",
    "arxiv_id": "quant-ph/0311017",
    "authors": [
      "Roman Orus",
      "Jose I. Latorre"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "hep-th"
    ],
    "doi": "10.1103/PhysRevA.69.052308",
    "journal_ref": "Phys.Rev. A69 (2004) 052308",
    "title": "Universality of Entanglement and Quantum Computation Complexity",
    "url": "https://arxiv.org/abs/quant-ph/0311017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cb59108d-91c2-4f72-b7db-63a48b7af7b4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}