Ising spin echo ($e^{-i{H}_I\tau /2}P{e}^{-i{H}_I\tau /2}{P}^{†}=I$)

A $\pi$ rotation about the x-axis on one qubit conjugates $Z\otimes Z$ to its negative. With ideal instantaneous pulses, two equal free-evolution intervals separated by this pulse and its inverse cancel an Ising coupling exactly. Finite-duration pulses require accounting for the coupling during the pulses; the error is small only when $|J|$ times the pulse duration is small, or when the control is explicitly designed to compensate it.