 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-2/10e/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The equality

f (x) = 4

holds exactly for

x \equiv 1 (mod 3)

. Projecting onto the measured second-register value and normalizing gives

∣ α ⟩ = \frac{1}{2} (∣1 ⟩ + ∣4 ⟩ + ∣7 ⟩ + ∣10 ⟩) .

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