Grover's Algorithm
Iteration 0 / 3
P(target) 6.25%
Phase Initial
Initial Superposition
Classical queriesO(16)
Grover queriesO(3)
≈ 5.3× faster
Target State
|0111⟩ = 7
Parameters
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Oracle
Flips the phase of the target state: |target⟩ → −|target⟩. This marks the correct answer without revealing it — the amplitude magnitude is unchanged, only the sign.

Diffusion
Reflects all amplitudes around their mean ⟨α⟩. Below-mean states grow; above-mean states shrink. Because the target was flipped it is now far below mean — so it gains the most amplitude each iteration.

Convergence
After ⌊π√N/4⌋ iterations the state vector aligns with |target⟩ and measurement succeeds with near-certainty.
Further Reading
Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. Proc. 28th ACM STOC, pp. 212–219. arXiv:quant-ph/9605043 ↗
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ITER0/3
P(TARGET)6.25%
FPS60
Grover's Algorithm
Interactive visualization of quantum amplitude amplification.
Watch how interference steers probability toward the target state
through oracle phase-flips and diffusion inversions.