 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-3/15d/c/solution

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

Use three controlled-NOT gates with control-target directions

1 ⟶ 2, 2 ⟶ 1, 1 ⟶ 2.

On computational-basis bits they act as

(x, y) ⟼ (x, x \oplus y) ⟼ (y, x \oplus y) ⟼ (y, x) .

They therefore implement the Three-CNOT decomposition of the SWAP gate, and linearity proves the identity on every two-qubit state.

 New to topics? Read the docs here!