{
  "annotation_id": "4e3bda7e-e1a4-46a9-9247-edbfd5cc004e",
  "date_created": "2026-03-02T18:02:34.696000Z",
  "date_modified": "2026-03-02T18:02:34.696000Z",
  "file_hash": "0a53ca380d83e193bdeafee5fcc67069b623e027b60a4dee7aca2e21b03d1d30",
  "private": false,
  "record": {
    "abstract": "The design of time-independent local Hamiltonians that realise quantum\nalgorithms is derived from the study of perfect state transfer. The novel\nfeatures of this evolution are the perfect realisation of the computation, and\nthe ability to implement operations in parallel rather than sequentially. This\nis applied to a quantum circuit for concatenated error correcting codes, and\nthe properties of the eigenstates are compared to those of topological\nmemories. An erroneous implementation of the algorithm (one where a single\nerror could lead to a fault in the output) is found not to be topological,\nwhereas a true fault-tolerant algorithm possesses self-correcting properties,\nsuggesting the existence of a unifying structure for fault-tolerant memories.",
    "arxiv_id": "quant-ph/0702092",
    "authors": [
      "Alastair Kay"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The Topological Properties of Fault-Tolerant Circuits",
    "url": "https://arxiv.org/abs/quant-ph/0702092"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "85191aed-c863-4eec-9bab-9e3e2b513731",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}