Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 10C / a / Solution

Write $x=x_1{x}_2$. Since the marked word is $11$, the required oracle is a single Toffoli gate with $x_1$ and $x_2$ as its two controls and the answer qubit $y$ as its target:The target flips exactly when both controls are one, which is exactly when $x=11$.