A quantum search algorithm that finds a target item in an unsorted database in O(√N) operations vs the classical O(N) — a quadratic speedup for any problem expressible as 'search a space for an item satisfying some condition'.
Grover's Algorithm, discovered by Lov Grover in 1996, uses amplitude amplification to repeatedly increase the probability of measuring the correct answer. It's NOT exponentially faster than classical search (unlike Shor's algorithm for factoring), but the quadratic speedup applies very broadly — any NP problem can be 'Grover-accelerated' to sqrt-time. The catch: this is still exponential in problem size, just with a smaller exponent.
Searching a 1-million-item unsorted database in 1,000 quantum operations (~√1M) instead of the 500,000 average comparisons classical search would require.
Grover's quadratic speedup is more broadly applicable than Shor's exponential speedup — but the practical benefit requires enough qubits to make the speedup outpace the constant-factor overhead of quantum operations.
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