{
  "annotation_id": "38178d41-5d07-48bf-890b-d4d3370ec954",
  "date_created": "2026-03-02T18:02:06.147000Z",
  "date_modified": "2026-03-02T18:02:06.147000Z",
  "file_hash": "27775a71ed0fc1e621675559cf444c4d631cce46fedc2a67be0ca71555b51c03",
  "private": false,
  "record": {
    "abstract": "The one-way quantum computing model introduced by Raussendorf and Briegel\n[Phys. Rev. Lett. 86 (22), 5188-5191 (2001)] shows that it is possible to\nquantum compute using only a fixed entangled resource known as a cluster state,\nand adaptive single-qubit measurements. This model is the basis for several\npractical proposals for quantum computation, including a promising proposal for\noptical quantum computation based on cluster states [M. A. Nielsen,\narXiv:quant-ph/0402005, accepted to appear in Phys. Rev. Lett.]. A significant\nopen question is whether such proposals are scalable in the presence of\nphysically realistic noise. In this paper we prove two threshold theorems which\nshow that scalable fault-tolerant quantum computation may be achieved in\nimplementations based on cluster states, provided the noise in the\nimplementations is below some constant threshold value. Our first threshold\ntheorem applies to a class of implementations in which entangling gates are\napplied deterministically, but with a small amount of noise. We expect this\nthreshold to be applicable in a wide variety of physical systems. Our second\nthreshold theorem is specifically adapted to proposals such as the optical\ncluster-state proposal, in which non-deterministic entangling gates are used. A\ncritical technical component of our proofs is two powerful theorems which\nrelate the properties of noisy unitary operations restricted to act on a\nsubspace of state space to extensions of those operations acting on the entire\nstate space.",
    "arxiv_id": "quant-ph/0405134",
    "authors": [
      "Michael A. Nielsen",
      "Christopher M. Dawson"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.71.042323",
    "title": "Fault-tolerant quantum computation with cluster states",
    "url": "https://arxiv.org/abs/quant-ph/0405134"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4fef8db2-2776-442f-81ab-3725f8de87cd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}