{
  "annotation_id": "f9356525-625e-47f5-aea7-e2b36c4a686d",
  "date_created": "2026-03-02T18:02:37.495000Z",
  "date_modified": "2026-03-02T18:02:37.495000Z",
  "file_hash": "f92fe6e8befa3e8c64348addb513d4725c040725a918b508e63ab936ea39a875",
  "private": false,
  "record": {
    "abstract": "We solve a problem, which while not fitting into the usual paradigm, can be\nviewed as a quantum computation. Suppose we are given a quantum system\ndescribed by an N dimensional Hilbert space with a Hamiltonian of the form $E\n|w \u003e\u003c w|$ where $| w\u003e$ is an unknown (normalized) state. We show how to\ndiscover $| w \u003e$ by adding a Hamiltonian (independent of $| w \u003e$) and evolving\nfor a time proportional to $N^{1/2}/E$. We show that this time is optimally\nshort. This process is an analog analogue to Grover\u0027s algorithm, a computation\non a conventional (!) quantum computer which locates a marked item from an\nunsorted list of N items in a number of steps proportional to $N^{1/2}$.",
    "arxiv_id": "quant-ph/9612026",
    "authors": [
      "Edward Farhi",
      "Sam Gutmann"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An Analog Analogue of a Digital Quantum Computation",
    "url": "https://arxiv.org/abs/quant-ph/9612026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3b8f1bc4-167c-420c-9584-d134d560e53c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}