 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 324

A <graph state> has computational-basis expansion
$$
|G\rangle=\frac1{2^{|V|/2}}
\sum_{x\in\{0,1\}^{|V|}}
(-1)^{\sum_{(r,s)\in E}x_rx_s}|x\rangle.
$$
For the path $G_A$ with edges $(1,2)$ and $(2,3)$,
$$
\boxed{
|G_A\rangle=\frac1{\sqrt8}(
|000\rangle+|001\rangle+|010\rangle-|011\rangle
+|100\rangle+|101\rangle-|110\rangle+|111\rangle)}.
$$
For the triangle $G_B$, the extra edge $(3,1)$ changes the phase whenever $x_1=x_3=1$, giving
$$
\boxed{
|G_B\rangle=\frac1{\sqrt8}(
|000\rangle+|001\rangle+|010\rangle-|011\rangle
+|100\rangle-|101\rangle-|110\rangle-|111\rangle)}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 324 / 4 / b / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 324 / 4 / b / i / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 324 / 4 / b / i / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)