 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/10e/b/solution

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

The controlled phases and final bit reversal implement QFT. Thus

∣000 ⟩ \mapsto 2^{- 3/2} \sum_{j = 0}^{7} ∣ j ⟩

, while

∣011 ⟩ \mapsto 2^{- 3/2} \sum_{j = 0}^{7} e^{2 πi (3 j) /8} ∣ j ⟩,

which agrees with

QFT_{8} ∣0 ⟩

and

QFT_{8} ∣3 ⟩

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