{
  "annotation_id": "0a4109c5-3c77-4297-9471-b37223a4c98d",
  "date_created": "2026-03-02T18:02:34.534000Z",
  "date_modified": "2026-03-02T18:02:34.534000Z",
  "file_hash": "bd798baff5031b3e6ce99ada00b9a658bf54b11d367dd821d5eda0ac08c31775",
  "private": false,
  "record": {
    "abstract": "We consider a model of computation motivated by possible limitations on\nquantum computers. We have a linear array of n wires, and we may perform\noperations only on pairs of adjacent wires. Our goal is to build a circuits\nthat perform specified operations spanning all n wires. We show that the\nnatural lower bound of n-1 on circuit depth is nearly tight for a variety of\nproblems, and we prove linear upper bounds for additional problems. In\nparticular, using only gates adding a wire (mod 2) into an adjacent wire, we\ncan realize any linear operation in GL_n(2) as a circuit of depth 5n. We show\nthat some linear operations require depth at least 2n+1.",
    "arxiv_id": "quant-ph/0701194",
    "authors": [
      "Samuel A. Kutin",
      "David Petrie Moulton",
      "Lawren M. Smithline"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Computation at a distance",
    "url": "https://arxiv.org/abs/quant-ph/0701194"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9d246e7f-9ab8-465a-a8e4-4953bb454c1b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}