 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-4/10c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

For

ω = e^{2 πi / N}

QFT_{N} ∣ x ⟩ = \frac{1}{N} \sum_{y = 0}^{N - 1} ω^{x y} ∣ y ⟩ .

Its matrix is unitary because character orthogonality for the cyclic group gives orthogonal rows.

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