Grover's algorithm searches N items for a marked one in about √N queries. Its oracle marks the item with a minus sign. A sign alone changes no outcome, so each round follows the oracle with a *diffusion*: a reflection of every amplitude about the average of all of them.

After the oracle, the marked amplitude is negative and the average falls a little below the others. Reflecting about the average lifts the marked amplitude well above the rest. Repeated about (π/4)√N times, the marked item comes up with probability close to 1. For N = 4 one round is exact: the outcome is the marked item every time.

The diffusion is a sign on |0…0⟩ between two layers of Hadamards. The Studio's example "Grover search, 3 qubits" runs two rounds on N = 8: the marked item comes up with probability 121/128.

This exercise asks for no gates that cancel: the critique's smells are part of the check. `wai-quantum critique` lists them with their lines, and **What went wrong?** quotes them.