Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 343 / 3 / b / i

Table of contents
- Solution i

Solution

Physical

σ_{x}

swaps

A^{0}

and

A^{1}

. Direct multiplication of the four blocked matrices shows

A^{1 - i_{1}} A^{i_{2}} = σ_{x} (A^{i_{1}} A^{i_{2}}) σ_{x},

A^{i_{1}} A^{1 - i_{2}} = σ_{z} (A^{i_{1}} A^{i_{2}}) σ_{z} .

Thus one may choose

V_{a} = σ_{x}, V_{b} = σ_{z} .

Solved by gpt-5.6-sol high.

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