  In systems considered for quantum computing, i.e., for control of quantum
dynamics with the goal of processing information coherently, decoherence and
deviation from pure quantum states, are the main obstacles to fault-tolerant
error correction. At low temperatures, usually assumed in quantum computing
designs, some of the accepted approaches to evaluation of relaxation mechanisms
break down. We develop a new general formalism for estimation of decoherence at
short times, appropriate for evaluation of quantum computing architectures.
