Abstract We study a two-electron quantum dot molecule subjected to an uniform magnetic field and in a time-dependent electric field under the adiabatic approximation. The time-dependent spin exchange energy J( t) provides a possible realization for logic gates in quantum computer. Switching between the states is best achieved by the time. As the exchange coupling is tuned by changing the time-dependent electric field, thermal or other types of fluctuations in the experimental environment of system will lead to fluctuations in the exchange, thus causing error in the exchange-based swap gate, which is crucial for two qubit operations. We study the fluctuation effects on the exchange.