  We study the corrections to adiabatic dynamics of two coupled quantum dot
spin-qubits, each dot singly occupied with an electron, in the context of a
quantum computing operation. Tunneling causes double occupancy at the
conclusion of an operation and constitutes a processing error. We model the
gate operation with an effective two-level system, where non-adiabatic
transitions correspond to double occupancy. The model is integrable and
possesses three independent parameters. We confirm the accuracy of Dykhne's
formula, a nonperturbative estimate of transitions, and discuss physically
intuitive conditions for its validity. Our semiclassical results are in
excellent agreement with numerical simulations of the exact time evolution. A
similar approach applies to two-level systems in different contexts.
