  Geometric phases arise naturally in a variety of quantum systems with
observable consequences. They also arise in quantum computations when dressed
states are used in gating operations. Here we show how they arise in these
gating operations and how one may take advantage of the dressed states
producing them. Specifically, we show that that for a given, but arbitrary
Hamiltonian, and at an arbitrary time {\tau}, there always exists a set of
dressed states such that a given gate operation can be performed by the
Hamiltonian up to a phase {\phi}. The phase is a sum of a dynamical phase and a
geometric phase. We illustrate the new phase for several systems.
