 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/10d/c/solution

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

The offset state is

S^{x_{0}}

applied to the offset-zero periodic state. Part (b) therefore makes its QFT output distribution independent of

x_{0}

. Explicitly, only outcomes divisible by

A = N / r

occur, each with probability

1/ r

;

x_{0}

contributes only a phase.

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