  The geometric and open path phases of a four-state system subject to time
varying cyclic potentials are computed from the Schr\"{o}dinger equation. Fast
oscillations are found in the non-adiabatic case. For parameter values such
that the system possesses degenerate levels, the geometric phase becomes
anomalous, undergoing a sign switch. A physical system to which the results
apply is a molecular dimer with two interacting electrons. Additionally, the
sudden switching of the geometric phase promises to be an efficient control in
two-qubit quantum computing.
