Ex10 23

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.23}$

a) Check that each of the cluster states of examples 10.2.7, 10.2.8, and 10.2.9 is stabilized by the operators of Equation 10.7.

b) Find the cluster state for the $1\times 5$ lattice.

b) Find the cluster state for the $2\times 2$ lattice.