 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-1/10c/b/solution

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

For every product vector,

(A \otimes B) (∣ x ⟩ \otimes ∣ y ⟩) = A ∣ x ⟩ \otimes B ∣ y ⟩ .

Product vectors span the two-register state space, so the single

A \otimes B

gate equals parallel application of

A

to the first register and

B

to the second. Unitarity guarantees that both descriptions are valid quantum circuits.

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