 Solution

Write $X={\sigma }_x$, $Y={\sigma }_y$, $Z={\sigma }_z$. The specified diagonal two-qubit gate has the exact factorizationThus one exact implementation is to set the controllable Ising coupling to zero and perform the two local rotations about the z-axis, synthesized from the available $x,y$ pulses as in part (c). Alternatively, turn off the local fields and choose the interaction area $\int J_{12}(t)dt=\pi /2$. Thenwhich implements the same physical gate up to global phase. The printed gate is local, not entangling; the pulse construction does not change that fact.