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    "id": "grover-unstructured-quantum-search-1996",
    "title": "Grover: square-root quantum search",
    "summary": "Grover gives a quantum algorithm for finding a unique marked item in an unstructured search space using order sqrt(N) oracle iterations, by combining a conditional phase flip with inversion about the average amplitude.\n\nFinding one marked item among an unsorted set usually takes a number of classical checks proportional to the set size. Grover uses quantum interference to raise the chance of observing the marked item after roughly a square-root number of oracle calls. A phase flip marks the desired state; reflection about the average amplitude then reinforces it. The method requires a coherent condition check that leaves no unwanted trace of the search path. Its query advantage is quadratic, not an automatic exponential acceleration of every computing task. For a search space of 2^n candidates, the remaining cost can still be exponential in n. The number of repetitions matters: continuing indefinitely can lower success again. The exact 1996 revised paper covers the unique-marked setting and discusses extensions; the companion BBHT analysis supplies explicit timing and an unknown-count procedure. Neither paper demonstrates a deployed database or removes the cost of building the oracle.",
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    "area": "Quantum search and query complexity",
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        "description": "The assessed search uses a coherent reversible oracle, uniform preparation and controlled phase/reflection operations, initially for one marked state among N=2^n possibilities. The O(sqrt(N)) improvement counts oracle queries, excluding oracle construction, physical access and nonquery resource costs. Success oscillates with iteration count. Detailed unknown-solution-count timing belongs to the separately credited BBHT work. This does not solve arbitrary NP problems in polynomial time or demonstrate quantum hardware. WRS has not certified a complete optimality proof or implementation.",
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        {
          "citation": "Boyer, Brassard, Hoyer and Tapp, Tight bounds on quantum searching, exact1996arXivv1",
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        {
          "citation": "Grover exactv3 repository identity and version history",
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      "statement": "# Grover: square-root quantum search\n\nGrover gives a quantum algorithm for finding a unique marked item in an unstructured search space using order sqrt(N) oracle iterations, by combining a conditional phase flip with inversion about the average amplitude.\n\nFinding one marked item among an unsorted set usually takes a number of classical checks proportional to the set size. Grover uses quantum interference to raise the chance of observing the marked item after roughly a square-root number of oracle calls. A phase flip marks the desired state; reflection about the average amplitude then reinforces it. The method requires a coherent condition check that leaves no unwanted trace of the search path. Its query advantage is quadratic, not an automatic exponential acceleration of every computing task. For a search space of 2^n candidates, the remaining cost can still be exponential in n. The number of repetitions matters: continuing indefinitely can lower success again. The exact 1996 revised paper covers the unique-marked setting and discusses extensions; the companion BBHT analysis supplies explicit timing and an unknown-count procedure. Neither paper demonstrates a deployed database or removes the cost of building the oracle.\n\n## Scientific scope\n\nThe assessed search uses a coherent reversible oracle, uniform preparation and controlled phase/reflection operations, initially for one marked state among N=2^n possibilities. The O(sqrt(N)) improvement counts oracle queries, excluding oracle construction, physical access and nonquery resource costs. Success oscillates with iteration count. Detailed unknown-solution-count timing belongs to the separately credited BBHT work. This does not solve arbitrary NP problems in polynomial time or demonstrate quantum hardware. WRS has not certified a complete optimality proof or implementation.\n\n## People and systems\n\nLov K. Grover\n\n\n\n## Original sources\n\n- [Grover, A fast quantum mechanical algorithm for database search, exact1996arXivv3](https://arxiv.org/pdf/quant-ph/9605043v3)\n- [Boyer, Brassard, Hoyer and Tapp, Tight bounds on quantum searching, exact1996arXivv1](https://arxiv.org/pdf/quant-ph/9605034v1)\n- [Grover exactv3 repository identity and version history](https://arxiv.org/abs/quant-ph/9605043v3)\n",
      "summary": "Grover gives a quantum algorithm for finding a unique marked item in an unstructured search space using order sqrt(N) oracle iterations, by combining a conditional phase flip with inversion about the average amplitude.\n\nFinding one marked item among an unsorted set usually takes a number of classical checks proportional to the set size. Grover uses quantum interference to raise the chance of observing the marked item after roughly a square-root number of oracle calls. A phase flip marks the desired state; reflection about the average amplitude then reinforces it. The method requires a coherent condition check that leaves no unwanted trace of the search path. Its query advantage is quadratic, not an automatic exponential acceleration of every computing task. For a search space of 2^n candidates, the remaining cost can still be exponential in n. The number of repetitions matters: continuing indefinitely can lower success again. The exact 1996 revised paper covers the unique-marked setting and discusses extensions; the companion BBHT analysis supplies explicit timing and an unknown-count procedure. Neither paper demonstrates a deployed database or removes the cost of building the oracle.",
      "title": "Grover: square-root quantum search"
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    "id": "grover-unstructured-quantum-search-1996",
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    "title": "Grover: square-root quantum search",
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    "evidence_summary": "Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.",
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      {
        "title": "Grover, A fast quantum mechanical algorithm for database search, exact 1996 ar Xivv 3",
        "url": "https://arxiv.org/pdf/quant-ph/9605043v3",
        "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits."
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        "title": "Boyer, Brassard, Hoyer and Tapp, Tight bounds on quantum searching, exact 1996 ar Xivv 1",
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