Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 10D / c

Table of contents
- Solution c

Solution

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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