{
  "annotation_id": "d90faf0f-c31a-4c59-b557-af92ccf80494",
  "date_created": "2026-03-02T18:01:49.025000Z",
  "date_modified": "2026-03-02T18:01:49.025000Z",
  "file_hash": "d812e49ced05b11e93afc6c68a698f6139345fb12611d7d734393a9d206995ec",
  "private": false,
  "record": {
    "abstract": "Assuming a cloning oracle, satisfiability, which is an NP complete problem,\nis shown to belong to $BPP^C$ and $BQP^C$ (depending on the ability of the\noracle C to clone either a binary random variable or a qubit). The same result\nis extended in the case of an approximate cloning oracle, thus establishing\nthat $NP \\subseteq BPP^C \\subseteq BQP^C$ and $NP \\subseteq BPP^{AC} \\subseteq\nBQP^{AC}$, where C and AC are the exact and approximate cloning oracles,\nrespectively. Although exact cloning is impossible in quantum systems,\napproximate cloning remains a possibility. However, the best known methods for\napproximate cloning (based on unitary evolution) do not currently achieve the\ndesired precision levels. And it remains an open question whether they could be\nimproved when non-linear (or non-unitary) operators are used. Finally, a\nstraightforward attempt to dispense with cloning, replacing it by unitary\nevolution, is proved to be impossible.",
    "arxiv_id": "quant-ph/0112133",
    "authors": [
      "John A. Drakopoulos",
      "Theodore N. Tomaras"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Using Cloning to Solve NP Complete Problems",
    "url": "https://arxiv.org/abs/quant-ph/0112133"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "86027d67-3f00-49df-89d9-7efa6d5e2657",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}