 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-3/15d/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The value

3

occurs at

x = 1, 5, 9

. Projecting onto that measurement outcome and normalizing leaves the periodic coset state

∣ α ⟩ = \frac{1}{3} (∣1 ⟩ + ∣5 ⟩ + ∣9 ⟩) .

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