{
  "annotation_id": "490f40b5-b3cf-496b-b4ba-ec6a2e66942e",
  "date_created": "2026-03-02T18:02:06.144000Z",
  "date_modified": "2026-03-02T18:02:06.144000Z",
  "file_hash": "28ebf9d4f868cc147c66b92fb9b211224357f8e2223e4f6fea68097840303818",
  "private": false,
  "record": {
    "abstract": "We consider the problem of searching a d-dimensional lattice of N sites for a\nsingle marked location. We present a Hamiltonian that solves this problem in\ntime of order sqrt(N) for d\u003e2 and of order sqrt(N) log(N) in the critical\ndimension d=2. This improves upon the performance of our previous quantum walk\nsearch algorithm (which has a critical dimension of d=4), and matches the\nperformance of a corresponding discrete-time quantum walk algorithm. The\nimprovement uses a lattice version of the Dirac Hamiltonian, and thus requires\nthe introduction of spin (or coin) degrees of freedom.",
    "arxiv_id": "quant-ph/0405120",
    "authors": [
      "Andrew M. Childs",
      "Jeffrey Goldstone"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.70.042312",
    "journal_ref": "Phys. Rev. A 70, 042312 (2004)",
    "title": "Spatial search and the Dirac equation",
    "url": "https://arxiv.org/abs/quant-ph/0405120"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e11c7b77-5693-4dd5-873a-f8e02e084bfc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}