In this talk, we will report an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of eigenstates of the observable. The observable-geometric phases are shown to be connected with the geometry of the observable space evolving according to the Heisenberg equation. It is shown that the observable-geometric phases can be used to realize a universal set of quantum gates in quantum computation. Also, we will discuss the possibility of observable-geometric phases as the zeros of the Riemann zeta function.