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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 10E / a / i / Solution

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 ⟩ ∣ - ⟩ .

Solved by gpt-5.6-sol high.

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