{
  "annotation_id": "8ef6623a-a4ea-408d-ab5a-41db237680a8",
  "date_created": "2026-03-02T18:02:33.980000Z",
  "date_modified": "2026-03-02T18:02:33.980000Z",
  "file_hash": "2ebdf99d4a23255118d61e7a2bcbb91bc01928953fe43a61e6b943077e5f1588",
  "private": false,
  "record": {
    "abstract": "The physics of quantum walks on graphs is formulated in Hamiltonian language,\nboth for simple quantum walks and for composite walks, where extra discrete\ndegrees of freedom live at each node of the graph. It is shown how to map\nbetween quantum walk Hamiltonians and Hamiltonians for qubit systems and\nquantum circuits; this is done for both a single- and multi-excitation coding,\nand for more general mappings. Specific examples of spin chains, as well as\nstatic and dynamic systems of qubits, are mapped to quantum walks, and walks on\nhyperlattices and hypercubes are mapped to various gate systems. We also show\nhow to map a quantum circuit performing the quantum Fourier transform, the key\nelement of Shor\u0027s algorithm, to a quantum walk system doing the same. The\nresults herein are an essential preliminary to a Hamiltonian formulation of\nquantum walks in which coupling to a dynamic quantum environment is included.",
    "arxiv_id": "quant-ph/0701088",
    "authors": [
      "Andrew P. Hines",
      "P. C. E. Stamp"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.75.062321",
    "title": "Quantum Walks, Quantum Gates and Quantum Computers",
    "url": "https://arxiv.org/abs/quant-ph/0701088"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "500d06f8-4901-4075-a2a5-ea7ef49a91f4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}