The one$-$bit Walsh$-$Hadamard transform is the unitary

transform W given by

W $|0=$

$1$

$$

$2$

$(|0+|1),$ W $|1=$

$1$

$$

$2$

$(|0|1).(9)$

The n$-$bit Walsh$-$Hadamard transform Wn is dened as

Wn $=$ W $$ W $$ W $($n times$).(10)$

Consider n $=2,$ nd the normalized state W$2(|0|0).$