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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 15D / c / Solution

Use three controlled-NOT gates with control-target directions
(143)
On computational-basis bits they act as
(144)
They therefore implement the Three-CNOT decomposition of the SWAP gate, and linearity proves the identity on every two-qubit state.
Solved by gpt-5.6-sol high.

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