{
  "annotation_id": "80b471e2-ee02-4045-ac7d-c9f0e74c009a",
  "date_created": "2026-03-02T18:02:05.749000Z",
  "date_modified": "2026-03-02T18:02:05.749000Z",
  "file_hash": "702e1d4df9ca54d15d403fc8907b461757ed0ed16d636e48a90935720caa8a69",
  "private": false,
  "record": {
    "abstract": "While the question ``how many CNOT gates are needed to simulate an arbitrary\ntwo-qubit operator\u0027\u0027 has been conclusively answered -- three are necessary and\nsufficient -- previous work on this topic assumes that one wants to simulate a\ngiven unitary operator up to global phase. However, in many practical cases\nadditional degrees of freedom are allowed. For example, if the computation is\nto be followed by a given projective measurement, many dissimilar operators\nachieve the same output distributions on all input states. Alternatively, if it\nis known that the input state is |0\u003e, the action of the given operator on all\northogonal states is immaterial. In such cases, we say that the unitary\noperator is incompletely specified; in this work, we take up the practical\nchallenge of satisfying a given specification with the smallest possible\ncircuit. In particular, we identify cases in which such operators can be\nimplemented using fewer quantum gates than are required for generic completely\nspecified operators.",
    "arxiv_id": "quant-ph/0401162",
    "authors": [
      "Vivek V. Shende",
      "Igor L. Markov"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "V. V. Shende and I. L. Markov, Quantum Circuits For Incompletely\n  Specified Two-Qubit Operators, Quantum Information \u0026 Computation 5, pp.\n  048-056 (2005)",
    "title": "Quantum Circuits for Incompletely Specified Two-Qubit Operators",
    "url": "https://arxiv.org/abs/quant-ph/0401162"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "55c33be1-31d7-43b9-8842-de260955bc66",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}