time evolution operator (quantum gates)

[eyal]

Hi,

Can anyone please show me how do i use the time evolution operator (V) applied on the ground state [g> and getting the same result as in the image below?
i need to show the explicit calculation..

 

taken from - from Cirac & Zoller, Quantum Computations with Cold Trapped Ions


Thanks!!

[imatfaal]

!

Moderator Note

 

moved to homework help.

 

You should explain where you have got to and what you think is stopping your completion of the task