  We develop dynamical non-Markovian description of quantum computing in weak
coupling limit, in lowest order approximation. We show that long range memory
of quantum reservoir produces strong interrelation between structure of noise
and quantum algorithm, implying nonlocal attacks of noise. We then argue that
the quantum error correction method fails to protect quantum computation
against electromagnetic or phonon vacuum which exhibit $1/t^4$ memory. This
shows that the implicit assumption of quantum error correction theory --
independence of noise and self-dynamics -- fails in long time regimes. We also
use our approach to present {\it pure} decoherence and decoherence accompanied
by dissipation in terms of spectral density of reservoir. The so-called {\it
dynamical decoupling} method is discussed in this context. Finally, we propose
{\it minimal decoherence model}, in which the only source of decoherence is
vacuum. We optimize fidelity of quantum information processing under the
trade-off between speed of gate and strength of decoherence.
