Operation Time of Quantum Gates
  We consider a quantum gate 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 quantum-mechanical average energy, and theta is the phase shift modulo pi.   [We changed the name of a macro file to a more Windows-friendly one, and we clarified the remark "Note that..." after equation (4).] 
Lev B. Levitin, Tommaso Toffoli, Zachary Walton (Boston University,   ECE Dept.)