  A quantum system interacting with its environment is subject to dephasing
which ultimately destroys the information it holds. Using a superconducting
qubit, we experimentally show that this dephasing has both dynamic and
geometric origins. It is found that geometric dephasing, which is present even
in the adiabatic limit and when no geometric phase is acquired, can either
reduce or restore coherence depending on the orientation of the path the qubit
traces out in its projective Hilbert space. It accompanies the evolution of any
system in Hilbert space subjected to noise.
