{
  "annotation_id": "6d260242-bbeb-492f-8608-e31da43ebf27",
  "date_created": "2026-03-02T18:02:24.138000Z",
  "date_modified": "2026-03-02T18:02:24.138000Z",
  "file_hash": "58a8a7f3cef7044953dbffe423c29c5396cc2165cbd150c5130afac54bf948b8",
  "private": false,
  "record": {
    "abstract": "The standard quantum search algorithm lacks a feature, enjoyed by many\nclassical algorithms, of having a fixed-point, i.e. a monotonic convergence\ntowards the solution. Here we present two variations of the quantum search\nalgorithm, which get around this limitation. The first replaces selective\ninversions in the algorithm by selective phase shifts of $\\frac{\\pi}{3}$. The\nsecond controls the selective inversion operations using two ancilla qubits,\nand irreversible measurement operations on the ancilla qubits drive the\nstarting state towards the target state. Using $q$ oracle queries, these\nvariations reduce the probability of finding a non-target state from $\\epsilon$\nto $\\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead\nto robust quantum algorithms, and provide conceptually new schemes for error\ncorrection.",
    "arxiv_id": "quant-ph/0603132",
    "authors": [
      "Lov K. Grover",
      "Apoorva Patel",
      "Tathagat Tulsi"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Algorithms with Fixed Points: The Case of Database Search",
    "url": "https://arxiv.org/abs/quant-ph/0603132"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fe6fbe75-d5d7-47dd-9ed9-6bc02b6c8a3c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}