 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/10e/a/i/solution

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

Let

∣ - ⟩ = (∣0 ⟩ - ∣1 ⟩) / 2

. After the Hadamards and the oracle, Bernstein-Vazirani phase kickback gives

∣ Φ_{1} ⟩ = \frac{1}{2 ^{n /2}} x \in {0, 1}^{n} \sum (- 1)^{a \cdot x \oplus b} ∣ x ⟩ ∣ - ⟩ .

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