  This paper presents 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 quantum geometry
of the observable space evolving according to the Heisenberg equation. They are
indeed distinct from Berry's phase \cite{Berry1984, Simon1983} as the system
evolves adiabatically. It is shown that the observable-geometric phases can be
used to realize a universal set of quantum gates in quantum computation. This
scheme leads to the same gates as the Abelian geometric gates of Zhu and Wang
\cite{ZW2002,ZW2003}, but based on the quantum geometry of the observable space
beyond the state space.
