Using Mathematica, explicitly verify identities (4.26), for a four-qubit gate. Write a Mathematica script that implements the code, for an arbitrary input state |j 2, illustrated in panel (a) of Fig....

Using Mathematica, explicitly verify identities (4.26), for a four-qubit gate.

Write a Mathematica script that implements the code, for an arbitrary input

state |j 2, illustrated in panel (a) of Fig. 4.2. Construct a two-qubit swap operator,

and calculate the action of the swap operator on the output of this gate. Compare

your result with that of QFT |j 2.