Ex12 4

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 12.4}$

Show that the transversal circuit shown in Figure 12.8 does not implement the Toffoli gate. Consider the effect of the circuit on $\ket{\tilde 1}\otimes\ket{\tilde 0}\otimes\ket{\tilde 0}$.