Grover's Algorithm

Amplitude amplification for unstructured search: O(√N) oracle queries versus O(N) classical. Each Grover iteration applies the oracle O and diffusion operator D = 2|s⟩⟨s|−I to amplify the marked state.

Number of qubits n n=4, N=16 states

Target state |0101⟩ = 5

Iterations k k = 0

Iterations

Optimal k = ⌊π√N/4⌋

P(target)

Classical / Quantum queries

Success Rate