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

A final oracle call evaluates

f

on the definite input

a

:

∣ Φ_{3} ⟩ = (- 1)^{b} ∣ a ⟩ ∣1 \oplus f (a)⟩ = (- 1)^{b} ∣ a ⟩ ∣1 \oplus a \cdot a \oplus b ⟩ .

Since

a \cdot a

modulo two is the parity of the Hamming weight of

a

, this form also determines the last-qubit measurement.

Solved by gpt-5.6-sol high.

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