  We consider a quantum gate, driven by a general time-dependent Hamiltonian,
that complements the state of a qubit and then adds to it an arbitrary phase
shift. It is shown that the minimum operation time of the gate is tau =
(h/4E)(1+2 theta/pi), where h is Planck's constant, E is the average over time
of the quantum-mechanical average energy, and theta is the phase shift modulo
pi.
