Ex11 13

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 11.13}$

Suppose a single qubit $\ket\psi = a\ket 0 + b\ket 1$ has been encoded using the Steane code and that the error $E = \frac{1}{2}X_2 + \frac{\sqrt{3}}{2}Z_3$ has occurred. Write down

a)the encoded state,

b) the state after the error has occurred,

c) for each phase of the error correction the syndrome and the resulting state

d) each error correcting transformation applied and the state after each of these applications.