The intuition of this gate is best understood in terms of the picture given above. When the state of the system is | 11 ⟩ ⟩ , the pulses send the state around the Bloch sphere twice and accumulates a net phase ϕ ϕ 2 = 4 π π Δ Δ Δ Δ 2 + 2 Ω Ω 2 . When one of the atoms is in | 0 ⟩ ⟩ state, the other atom does not go around the Bloch sphere fully after the first pulse due to the mismatch in Rabi frequency. The second pulse corrects for this effect by rotating the state around a different axis. This puts the atom back into the | 1 ⟩ ⟩ state with a net phase ϕ ϕ 1 , which can be calculated easily. The pulses can be chosen to make e i ϕ ϕ 2 = e i ( 2 ϕ ϕ 1 + π π ) . Doing so makes this gate equivalent to a controlled-z gate up-to a local rotation. The truth table of Levine-Pichler gate is given on the right. This gate has been improved using the methods of quantum optimal controls recently.