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Coin flip

One qubit, one Hadamard — 0 and 1 in equal measure.

Bell state

The smallest entangled pair: only 00 and 11 ever appear.

GHZ state

Three qubits acting as one — counts split between 000 and 111.

W state

Exactly one excitation, shared three ways: 001, 010, 100 in equal thirds.

Grover search

One oracle call on two qubits — every shot lands on the marked item 11.

QFT of a basis state

Counts come out flat: the transform stores its result in phases, which sampling cannot see.

QAOA ring (p=1)

Shallow four-qubit ring ansatz — the workhorse of combinatorial optimization.

Quantum randomness

Four Hadamards, sixteen outcomes, uniform by physics rather than by algorithm.