{
  "annotation_id": "ef5a0194-23a0-48af-9741-c3038bf4681c",
  "date_created": "2026-03-02T18:01:59.940000Z",
  "date_modified": "2026-03-02T18:01:59.940000Z",
  "file_hash": "49338228b5e959cd78d76883796022cef01140218a6edca19035671c7ade4ec3",
  "private": false,
  "record": {
    "abstract": "This work proposes numerical tests which determine whether a two-qubit\noperator has an atypically simple quantum circuit. Specifically, we describe\nformulae, written in terms of matrix coefficients, characterizing operators\nimplementable with exactly zero, one, or two controlled-not (CNOT) gates and\nall other gates being one-qubit. We give an algorithm for synthesizing\ntwo-qubit circuits with optimal number of CNOT gates, and illustrate it on\noperators appearing in quantum algorithms by Deutsch-Josza, Shor and Grover. In\nanother application, our explicit numerical tests allow timing a given\nHamiltonian to compute a CNOT modulo one-qubit gates, when this is possible.",
    "arxiv_id": "quant-ph/0308045",
    "authors": [
      "Vivek V. Shende",
      "Stephen S. Bullock",
      "Igor L. Markov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.70.012310",
    "journal_ref": "Physical Review A 70, 012310 (2004)",
    "title": "Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing   Hamiltonians to Compute Controlled-Not Gates",
    "url": "https://arxiv.org/abs/quant-ph/0308045"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b195c1a8-2747-4764-b631-016c7633d25d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}