{
  "id": "quant-ph/0701194",
  "version": "v1",
  "published": "2007-01-26T19:48:41.000Z",
  "updated": "2007-01-26T19:48:41.000Z",
  "title": "Computation at a distance",
  "authors": [
    "Samuel A. Kutin",
    "David Petrie Moulton",
    "Lawren M. Smithline"
  ],
  "comment": "19 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform specified operations spanning all n wires. We show that the natural lower bound of n-1 on circuit depth is nearly tight for a variety of problems, and we prove linear upper bounds for additional problems. In particular, using only gates adding a wire (mod 2) into an adjacent wire, we can realize any linear operation in GL_n(2) as a circuit of depth 5n. We show that some linear operations require depth at least 2n+1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-26T19:48:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "computation",
      "linear operation",
      "adjacent wire",
      "linear upper bounds",
      "natural lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007quant.ph..1194K"
    }
  }
}