Two-Qubit Grover

Grover's algorithm searches an unstructured space of $N$ items in $O(\sqrt{N})$ steps. For $N = 4$ (two qubits) a single iteration finds the marked item with certainty. Each iteration has two parts:

1. Oracle — flip the sign (phase) of the marked basis state. To mark $|11\rangle$ we use a controlled-$Z$, since $CZ$ multiplies exactly $|11\rangle$ by $-1$.
2. Diffuser — reflect every amplitude about their mean ("inversion about the average"), amplifying the marked amplitude. The standard circuit is $H^{\otimes 2}\,X^{\otimes 2}\,CZ\,X^{\otimes 2}\,H^{\otimes 2}$.

Geometrically the two reflections rotate the state toward the marked item; for $N = 4$ that single rotation lands exactly on $|11\rangle$.

Try it

The starter code has the superposition and the diffuser — add the oracle that marks $|11\rangle$. The grader checks the output distribution, which should put all probability on $|11\rangle$.

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