Grover's Algorithm

Grover's algorithm, published by Lov Grover in 1996, provides a quadratic speedup for unstructured search. For a search space of N items, classical search requires O(N) queries while Grover's needs only O(√N) queries. The algorithm works by repeatedly applying the "Grover diffusion operator" — which amplifies the amplitude of the target state while suppressing others — through a process called amplitude amplification. After ~π√N/4 iterations, measuring the state yields the target item with high probability. Grover's algorithm is provably optimal — no quantum algorithm can do better for unstructured search. Applications include database search, solving NP-hard problems, and quantum cryptanalysis. HLQuantum includes a built-in Grover implementation.