= Solution
Write $X=\sigma_x$, $Y=\sigma_y$, $Z=\sigma_z$. The specified diagonal <two-qubit gate> has the exact factorization
$$
C_{\mathrm{phase}}=-Z\otimes Z=R_z(\pi)\otimes R_z(\pi).
$$
Thus 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 $\int J_{12}(t)dt=\pi/2$. Then
$$
U_I=e^{-i\pi Z\otimes Z/2}=-iZ\otimes Z=iC_{\mathrm{phase}},
$$
which implements the same physical gate up to <global phase>. \b[The printed gate is local, not entangling]; the pulse construction does not change that fact.
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