Evaluation of Decoherence for Quantum Computing Architectures: Qubit   System Subject to Time-Dependent Control
  We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantumcomputing gate function. The approximations are found to produce consistent results at short and intermediate times. 
Dmitry Solenov and Vladimir Privman