 Ising coupling of two qubits

An Ising coupling generates $e^{-i\varphi Z\otimes Z}$ with $\varphi =\int J(t)dt$ in units $\hslash =1$. It is entangling precisely when $\varphi$ is not an integer multiple of $\pi /2$. A $\pi$ rotation on one qubit reverses its sign, permitting an ideal echo to cancel an always-on coupling.