Ex11 16

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 11.16}$

Show that the operators $\tilde{X_i}$ as defined for stabilizer codes in Section \ref{stabPauliGates} act as a logical analog of the gates $X_i$ for the logical states obtained from the encoding $c$.