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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 15E / b / Solution

The state entering the controlled swap has lower-register states

∣ ϕ_{1} ⟩

and

V ∣ ϕ_{2} ⟩

. The swap test therefore gives

p_{0} = \frac{1}{2} (1 + ∣ ⟨ ϕ_{1} ∣ V ∣ ϕ_{2} ⟩ ∣^{2}) .

Solved by gpt-5.6-sol high.

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