2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90560We 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).]3 pages, Latex, Rinton-P9x6.cls and custom macros latex+3.tex as separate filesQuantum Physicstext